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Total result(s) found: 289
  • A. Kammonen and J. Kiessling and P. Plechac and M. Sandberg and A. Szepessy and R. Tempone. "Smaller generalization error derived for deep compared to shallow residual neural networks", arXiv preprint  arXiv:2010.01887, September 2020.​​​​​​​
Keywords:
residual network, deep random feature, supervised learning, error estimates, layer by layer algorithm.
  • Christian Bayer and Eric Joseph Hall and Raúl Tempone​. "Weak error rates for ​option pricing under the rough Bergomi model.​​" arXiv preprint arXiv:2009.01219​​​
Keywords:
Rough Bergomi, Weak error rate
  • Chiara Piazzola and Lorenzo Tamellini and Raúl Tempone,  "A note on tools for prediction under uncertainty and identifiability of SIR-like dynamical systems for epidemiology", arXiv preprint arXiv:2008.01400
Keywords:
Dynamical Systems, Mathematical Epidemiology, Uncertainty Quantification, Model Identifiability, Bayesian Inversion, Fisher Approximation
  • ​Chiheb Ben Hammouda,  Nadhir Ben Rached, and Raul Tempone. "Importance sampling for a robust and efficient multilevel Monte Carlo estimator for stochastic reaction networks.​"​ Statistics and Computing (2020): 1-25.​​​
Keywords:
Multilevel Monte Carlo. Continuous time Markov chains. Stochastic reaction networks. Stochastic biological systems. Importance sampling
Refereed Journals
  • Litvinenko, Alexander, Dimitry Logashenko, Raúl Tempone, Gabriel Wittum, and David Keyes. . "Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability". Int J Geomath 11, 10 (2020)
Keywords:
Uncertainty quantification·ug4·Multigrid·Density-driven flow· Reservoir·Groundwater·Salt formations
Refereed Journals
  • Beck, Joakim, Ben Mansour Dia, Luis Espath, Raúl Tempone. "Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design". Int J Numer Methods Eng. (2020); 121: 34823503
Keywords:
Electrical impedance tomography, Expected information gain, Importance sampling, Multilevel, Stochastic collocation
Refereed Journals
  • Bayer, Christian, Raúl Tempone, and Sören Wolfers, "Pricing American Options by Exercise Rate Optimization", Quantitative Finance, (2020)
Keywords:
Computational finance, American option pricing, stochastic optimization problem, Monte Carlo, multivariateapproximation, rough volatility
Refereed Journals
  • Hoel, Håkon, Gaukhar Shaimerdenova, and Raúl Tempone, "Multilevel Ensemble Kalman Filtering with local-level Kalman Gains", arXiv preprint 2002.00480
Keywords:
Stochastic differential and integral equations, Complexity and performance of numerical algorithms
  • Haji-Ali, Abdul-Lateef, Fabio Nobile, Raúl Tempone, and Sören Wolfers, "Multilevel weighted least squares polynomial approximation", ESAIM: M2AN, Volume 54, no. 2, (2020): 649–677

Keywords:
Multilevel methods, least squares approximation, multivariate approximation, polynomial approximation, convergence rates, error analysis
Refereed Journals
  • Ben Rached, Nadhir, Daniel MacKinlay, Zdravko Botev, Raúl Tempone, and Mohamed-Slim Alouini, "A Universal Splitting Estimator for the Performance Evaluation of Wireless Communications Systems", IEEE Transactions on Wireless Communications, 2020​
Keywords:
Rare event, performance evaluation, multilevel splitting algorithm, variance reduction
Refereed Journals
  • Ben Rached, Nadhir, Abla Kammoun, Mohamed-Slim Alouini, and Raúl Tempone, ​"An Accurate Sample Rejection Estimator of the Outage Probability With Equal Gain Combining"IEEE Open Journal of the Communications Society, Volume 1 (2020), Pages 1022-1034.
Keywords:
Outage probability, equal gain combining, importance sampling, sample rejection, generalised selection combining, bounded relative error.
Refereed Journals
  • ​Renzo Caballero, Ahmed Kebaier, Marco Scavino, and Raúl Tempone, "A Derivative Tracking Model for Wind Power Forecast Error", arXiv, 2006.15907​, 2020
Keywords:
Wind power, probabilistic forecasting, stochastic differential equations, Lamperti transform, numerical optimization, model selection, time-inhomogeneous Jacobi diffusion
  • Ballesio, Marco, Ajay Jasra, Erik von Schwerin, and Raúl Tempone; "A Wasserstein Coupled Particle Filter for Multilevel Estimation", arXiv, 2004.03981, 2020.
Keywords:
Filtering, Diffusions, Multilevel Monte Carlo, Particle Filters
  • Carlon, André Gustavo, Ben Mansour Dia, Luis Espath, Rafael Holdorf Lopez, Raúl Tempone, "Nesterov-aided stochastic gradient methods using Laplace approximation for Bayesian design optimization", Computer Methods in Applied Mechanics and Engineering, Volume 363, (2020).
Keywords:
Optimal experimental design, Bayesian inference, Laplace approximation, Stochastic optimization, Accelerated gradient descent, Importance sampling
Refereed Journals
Keywords:
Rough volatility, Monte Carlo, Adaptive sparse grids, Quasi Monte Carlo, Brownian bridge construction, Richardson extrapolation.
Refereed Journals
  • Bayer, Christian, Chiheb Ben Hammouda, and Raul Tempone. "Numerical smoothing and hierarchical approximations for efficient option pricing and density estimation." arXiv preprint arXiv:2003.05708 (2020).​
Keywords:
Deterministic quadrature methods, Hierarchical variance reduction methods, Multilevel Monte Carlo, Numerical smoothing, Adaptive sparse grids quadrature, Brownian bridge, Richardson extrapolation, Option pricing, Monte Carlo
  • ​Carlon, A.G., R.H. Lopez, L.F.R. Espath, L.F.F. Miguel, A.T. Beck, "A stochastic gradient approach for the reliability maximization of passively controlled structures", Engineering Structures, Volume 186 (2019), Pages 1-12.
Keywords:
Robust design, Reliability maximization, Stochastic gradient descent, Friction tuned mass dampers, Passive control
Refereed Journals
  • Litvinenko, Alexander, Abdulkadir C. Yucel, Hakan Bagci, Jesper Oppelstrup, Eric Michielssen, and Raúl Tempone. "Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method", in IEEE Journal on Multiscale and Multiphysics Computational Techniques, vol. 4, (2019), pp. 37-50
Keywords:
uncertainty quantification in geometry, random geometry, multilevel Monte Carlo method (MLMC), continuation MLMC, integral equation, fast multipole method (FMM), fast Fourier transform (FFT), scattering problem
Refereed Journals
  • ​Hoel, Håkon, and Anders Szepessy, "Classical Langevin Dynamics Derived from Quantum Mechanics", arXiv preprint 1906.09858
Keywords:
Stochastic methods, Quantum dynamics and nonequilibrium statistical mechanics, Stochastic differential and integral equations, Stochastic ordinary differential equations
  • ​Beck, Joakim, Lorenzo Tamellini, and Raúl Tempone, "IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains", Computer Methods in Applied Mathematics and Engineering, Volume 351 (2019): 330-350
Keywords:
Isogeometric analysis, Uncertainty quantification, Sparse grids, Stochastic collocation methods, Multilevel methods, Combination-technique
Refereed Journals
Keywords:
Multilevel Monte Carlo, Continuous time Markov chains, Stochastic reaction networks, Stochastic biological systems, Importance sampling
  • Bayer, Christian, Juho Häppölä, and Raúl Tempone. "Implied stopping rules for American basket options from Markovian projection." Quantitative Finance, 19(3), 371-390, (2019)
Keywords:
Basket option, Optimal stopping, Black–Scholes, Error bounds, Monte Carlo, Markovian projection, Hamilton–Jabcobi–Bellman
Refereed Journals
  • Jasra, Ajay, Seongil Jo, David Nott, Christine Shoemaker, and Raul Tempone. "Multilevel Monte Carlo in approximate Bayesian computation." Stochastic Analysis and Applications, Volume 37, no.3 (2019): 346-360.​
Keywords:
Approximate Bayesian computation, multilevel Monte Carlo, sequential Monte Carlo.
Refereed Journals
  • Issaid, Chaouki Ben, Mohamed-Slim Alouini, and Raul Tempone. "Eficient Monte Carlo Simulation of the Left Tail of Positive Gaussian Quadratic Forms." arXiv preprint arXiv:1901.09174 (2019).
Keywords:
Importance sampling, left tail, positive quadratic forms, Gaussian random vectors, bounded relative error.
  • Ballesio, Marco, Joakim Beck, Anamika Pandey, Laura Parisi, Erik von Schwerin, Raúl Tempone, "Multilevel Monte Carlo Acceleration of Seismic Wave Propagation under Uncertainty", ​​GEM - International Journal on Geomathematics, Volume 10, Issue 1, ​​(2019). p.22
Keywords:
Multilevel Monte Carlo, Propagation of Uncertainty, Seismic Wave Propagation, Partial Differential Equations with random data
Refereed Journals
  • Beck, Joakim, Ben Mansour Dia, Luis FR Espath, and Raul Tempone. "Multilevel Double Loop Monte Carlo and Stochastic Collocation Methods with Importance Sampling for Bayesian Optimal Experimental Design." arXiv preprint arXiv:1811.11469 (2018).​
Keywords:
Expected information gain, Laplace approximation, Importance sampling, Composite material, Stochastic collocation, Electrical impedance tomography
  • Clavijo, S. P., A. F. Sarmiento, L. F. R. Espath, Lisandro Dalcin, A. M. A. Cortes, and V. M. Calo. "Reactive n-species Cahn–Hilliard system: A thermodynamically-consistent model for reversible chemical reactions." Journal of Computational and Applied Mathematics 350 (2019): 143-154.​​​
Keywords:
Multicomponent Cahn–Hilliard, Chemical reactions, Isogeometric analysis, Spinodal decomposition
Refereed Journals
  • Babuska, Ivo, Zaid Sawlan, Marco Scavino, Barna Szabó, Raúl Tempone, "Spatial Poisson processes for fatigue crack initiation", Computer Methods in Applied Mechanics and Engineering, Volume 345, 1 March 2019, Pages 454-475.​​​​​​​​​​
Keywords:
Fatigue crack initiation, Linear elasticity, Notched metallic specimens, Spatial Poisson processes, Fatigue-limit models, Maximum likelihood methods
Refereed Journals
  • Beck, Joakim, Sören Wolfers, and Gerald P. Roberts: "Bayesian earthquake dating and seismic hazard assessment using chlorine-36 measurements (BED v1)", Geoscientific Model Development, 11, (2018), 4383–4397
Keywords:
Bayesian earthquake dating
Refereed Journals
  •  N. Ben Rached,  Z. Botev,  A. Kammoun, M.-S. Alouini, and R. Tempone,“Importance Sampling Estimator of Outage Probability under Generalized Selection Combining  Model”,  IEEE International Conference on Acoustics, Speech and Signal Processing, (ICASSP’2018), Calgary, Alberta, Canada, Apr. 2018.​
Keywords:
Outage probability, generalized selection combining, order statistics, Monte Carlo, importance sampling
Conference Proceedings
  • N. Ben Rached,  A. Kammoun, M.-S. Alouini, and R. Tempone,“Accurate Outage Probability Evaluation of Equal Gain Combining Receivers”,  IEEE Global Communications Conference (GLOBECOM’2018), Abu Dhabi, UAE, Dec. 2018.​
Keywords:
Outage probability, equal gain combining, importance sampling, sample rejection, bounded relative error.
Conference Proceedings
  • Rached, Nadhir Ben, Fatma Benkhelifa, Abla Kammoun, Mohamed-Slim Alouini, and Raul Tempone. "On the generalization of the hazard rate twisting-based simulation approach." Statistics and Computing 28, no. 1 (2018): 61-75.
Keywords:
Naive Monte Carlo, Rare events, Importance sampling, Hazard rate twisting, Logarithmic efficient, Twisting parameter.
Refereed Journals
  • Issaid, Chaouki Ben, Mohamed-Slim Alouini, and Raul Tempone. "On the Fast and Precise Evaluation of the Outage Probability of Diversity Receivers Over αμ , κμ , and ημ Fading Channels." IEEE Transactions on Wireless Communications 17, no. 2 (2018): 1255-1268.
Keywords:
—α−μ,κ−μ,η−μ, importance sampling,Monte Carlo, bounded relative error, outage probability, diversitytechniques.
Refereed Journals
  • Bayer, Christian, Markus Siebenmorgen, and Raul Tempone. "Smoothing the payoff for efficient computation of Basket option prices." Quantitative Finance 18, no. 3 (2018): 491-505.
Keywords:
Computational Finance, European option pricing, Multivariate approximation and integration, Sparse grids, Stochastic Collocation methods, Monte Carlo and Quasi Monte Carlo methods.
Refereed Journals
  • Issaid, Chaouki Ben, Mohamed-Slim Alouini, and Raul Tempone. "Efficient outage probability evaluation of diversity receivers over α-μ fading channels." In Wireless Communications and Networking Conference (WCNC), 2018 IEEE, pp. 1-6. IEEE, 2018.
Keywords:
—α − µ, importance sampling, Monte Carlo, bounded relative error, outage probability, diversity techniques
Refereed Journals
  • Rached, Nadhir Ben, Zdravko Botev, Abla Kammoun, Mohamed-Slim Alouini, and Raul Tempone. "Importance sampling estimator of outage probability under generalized selection combining model." In 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3909-3913. IEEE, 2018.​
Keywords:
Outage probability, generalized selection combining, order statistics, Monte Carlo, importance sampling.
Refereed Journals
  • Nobile, Fabio, Raul Tempone, and Sören Wolfers. "Sparse approximation of multilinear problems with applications to kernel-based methods in UQ." Numerische Mathematik 139, no. 1 (2018): 247-280.​
Keywords:
kernel-based methods in UQ
Refereed Journals
  • Iglesias, Marco, Zaid Sawlan, Marco Scavino, Raul Tempone, and Christopher Wood. "Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: Application to heat transfer in building walls." Inverse Problems 34, no. 7 (2018): 075008.​
Keywords:
Ensemble Kalman filter, linear PDEs, heat equation, nuisance boundary parameters marginalization, heat flux measurements, thermal resistance, heat capacity
Refereed Journals
  • Litvinenko, Alexander, Abdulkadir C. Yucel, Hakan Bagci, Jesper Oppelstrup, Eric Michielssen, and Raúl Tempone. "Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method." arXiv preprint arXiv:1809.00362 (2018).​
Keywords:
uncertainty quantification in geometry, random geometry, multilevel Monte Carlo method (MLMC), continuation MLMC, integral equation, fast multipole method (FMM), fast Fourier transform (FFT), scattering problem
  • Beck, Joakim, Lorenzo Tamellini, and Raúl Tempone. "IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains." arXiv preprint arXiv:1810.01661 (2018).​
Keywords:
Isogeometric analysis, Uncertainty Quantification, Sparse Grids, Stochastic Collocation methods, multilevel methods, combination-technique
  • Rached, Nadhir Ben, Zdravko Botev, Abla Kammoun, Mohamed-Slim Alouini, and Raul Tempone. "On the sum of order statistics and applications to wireless communication systems performances." IEEE Transactions on Wireless Communications 17, no. 11 (2018): 7801-7813.
Keywords:
Order statistics, outage probability, generalized selection combining, Monte Carlo, variance reduction techniques, importance sampling, conditional MC.
Refereed Journals
  • Bayer, Christian, Raúl Tempone, and Sören Wolfers. "Pricing American Options by Exercise Rate Optimization." arXiv preprint arXiv:1809.07300 (2018).​​​
Keywords:
Computational finance, American options, stochastic optimization, rough Bergomi,
  • Carlon, Andre Gustavo, Ben Mansour Dia, Luis FR Espath, Rafael Holdorf Lopez, and Raul Tempone. "Nesterov-aided Stochastic Gradient Methods using Laplace Approximation for Bayesian Design Optimization." arXiv preprint arXiv:1807.00653 (2018).​
Keywords:
Optimal Experimental Design, Bayesian Inference, Laplace Approximation, Stochastic Optimization, Accelerated Gradient Descent, Importance Sampling
  • Capriotti, Luca and Jiang, Yupeng and Shaimerdenova, Gaukhar, ''Approximation Methods for Inhomogeneous Geometric Brownian Motion'' (October 8, 2018). International Journal of Theoretical and Applied Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=3247379​
Keywords:
Inhomogeneous Geometric Brownian Motion; Constant Elasticity of Variance; Arrow-Debreu Security, Derivative Pricing; Power Series Expansions
Refereed Journals
  • Francisco, E. P., L. F. R. Espath, S. Laizet, and J. H. Silvestrini. "Reynolds number and settling velocity influence for finite-release particle-laden gravity currents in a basin." Computers & Geosciences 110 (2018): 1-9.​
Keywords:
Particle-laden gravity current, Energy budget, Deposition of particles, Direct numerical simulation
Refereed Journals
  • Bayer, Christian, Chiheb Ben Hammouda, and Raul Tempone. "Hierarchical adaptive sparse grids for option pricing under the rough Bergomi model." arXiv preprint arXiv:1812.08533(2018).
Keywords:
Rough volatility, Monte Carlo, Adaptive sparse grids, Brownian bridge construction, Richardson extrapolation
Keywords:
Ensemble Kalman Filter, Linear PDEs, Heat Equation, Nuisance Boundary Parameters Marginalization, Heat Flux Measurements, Thermal Resistance, Heat Capacity.
Refereed Journals
  • Tempone, Raúl, Sören Wolfers, "Smolyak’s algorithm: A powerful black box for the acceleration of scientific computations", In: Garcke J., Pflüger D., Webster C., Zhang G. (eds) Sparse Grids and Applications - Miami 2016. Lecture Notes in Computational Science and Engineering, vol 123.
Keywords:
Smolyak algorithm, sparse grids, hyperbolic cross approximation, combination technique, multilevel methods
  • Beck, Joakim, Ben Mansour Dia, Luis FR Espath, Quan Long, and Raul Tempone. "Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain." Computer Methods in Applied Mechanics and Engineering 334 (2018): 523-553​
Keywords:
Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain
Refereed Journals
  • ​Iglesias, Marco, Zaid Sawlan, Marco Scavino, Raul Tempone, and Christopher Wood. "Bayesian inferences of the thermal properties of a wall using temperature and heat flux measurements." International Journal of Heat and Mass Transfer 116 (2018): 417-431.
Keywords:
Heat Equation, Nuisance Boundary Parameters Marginalization, Heat Flux Measurements, Solid Walls, Bayesian Inference, Thermal Resistance, Heat Capacity, Experimental Design
Refereed Journals
  • N. Ben Rached, A. Kammoun, M.-S. Alouini, and R. Tempone, “A Unified Moment-Based Approach for the Evaluation of the Outage Probability with Noise and Interference”, IEEE Transactions on Wireless Communications, vol. 16, Issue 2, Feb.  2017.​
Keywords:
Moment-based approach, outage probability, generalized fading environment, interference, power series expansion, cross-moments, convergence study, selection diversity.
Refereed Journals
  • C. BenIssaid, N. Ben Rached, A. Kammoun, M.-S. Alouini, and R. Tempone, “On the Efficient Simulation of the Distribution of the Sum of Gamma-Gamma Variates with Application to the Outage Probability Evaluation Over Fading Channels”, IEEE Transactions on Communications, vol. 65, Issue 4, Apr. 2017​
Keywords:
Gamma-Gamma, generalized-K, importance sampling, Monte Carlo, bounded relative error, outage probability, diversity techniques.
Refereed Journals
  • Haji-Ali, Abdul-Lateef, and Raúl Tempone. "Multilevel and Multi-index Monte Carlo methods for the McKean–Vlasov equation." Statistics and Computing 28, no. 4 (2018): 923-935.​​​
Keywords:
Multi-index Monte Carlo, Multilevel Monte Carlo, Monte Carlo Particle systems, McKean–Vlasov Mean-field, Stochastic differential equations, Weak approximation, Sparse approximation, Combination technique.
Refereed Journals
  • Hoel, Hakon, Alexey Chernov, Kody Law, Fabio Nobile, and Raul Tempone. "Multilevel ensemble Kalman filtering for spatio-temporal processes." (2018)
Keywords:
Monte Carlo, multilevel, filtering, Kalman filter, ensemble Kalman filter, partial differential equations (PDE)
  • Litvinenko, Alexander, David Keyes, Venera Khoromskaia, Boris N. Khoromskij, and Hermann G. Matthies. "Tucker Tensor analysis of Matern functions in spatial statistics." arXiv preprint arXiv:1711.06874 (2017).
Keywords:
Fourier transform, low-rank tensor approximation, geostatistical optimal design, kriging, Matern covariance, Hilbert tensor, Kalman filter, Bayesian update, loglikelihood surrogate.
  • Francisco, Ezequiel P., L. F. R. Espath, and J. H. Silvestrini. "Direct numerical simulation of bi-disperse particle-laden gravity currents in the channel configuration." Applied Mathematical Modelling 49 (2017): 739-752.
Keywords:
Bi-disperse flows, Particle-laden gravity currents, Direct numerical simulation, Energy budget
Refereed Journals
  • Espath, L. F. R., A. F. Sarmiento, Lisandro Dalcin, and V. M. Calo. "On the thermodynamics of the Swift–Hohenberg theory." Continuum Mechanics and Thermodynamics 29, no. 6 (2017): 1335-1345.
Keywords:
Phase-field, Gradient theory, Thermodynamics of continua, Swift–Hohenberg theory
Refereed Journals
  • ​A. Litvinenko, HLIBCov: Parallel Hierarchical Matrix Approximation of Large Covariance Matrices and Likelihoods with Applications in Parameter Identification, https://arxiv.org/abs/1709.08625, 2017
Keywords:
HLIBPro, HLIBCov, parallel hierarchical matrices, approximating large covariance matrice, parameter estimation, Gaussian likelihood
  • ​​F. Nobile, R. Tempone, S. Wolfers, Multilevel weighted least squares polynomial approximation​, submitted arXiv:1707.00026 Oct. 2017​​
Keywords:
Multilevel methods, least squares approximation, multivariate approximation, polynomial approximation, error analysis
  • N. Rached, A. Kammoun, M. Alouini, R.Tempone, On the Efficient Simulation of the Left-Tail of the Sum of Correlated Log-normal Variates
Keywords:
On the Efficient Simulation of the Left-Tail of the Sum of Correlated Log-normal Variates
  • Nadhir Ben Rached, Abla Kammoun, Mohamed-Slim Alouini, Raul Tempone , On the Efficient Simulation of Outage Probability in a Log-normal Fading Environment,IEEE Transactions on Communications  65 Issue: 6  , 2017​

Keywords:
On the Efficient Simulation of Outage Probability in a Log-normal Fading Environment
Refereed Journals
  • F. Ruggeri, Z. Sawlan, M. Scavino, R. Tempone, A hierarchical Bayesian setting for an inverse problem in linear parabolic PDEs with noisy boundary conditions, Bayesian Analysis, Advance Publication, 12 May 2016. doi: 10.1214/16-BA1007​​​​​​
Keywords:
A hierarchical Bayesian setting for an inverse problem in linear parabolic PDEs with noisy boundary conditions
Refereed Journals
  • ​H. G. Matthies, A. Litvinenko, B. V. Rosic, E. Zander, Bayesian Parameter Estimation via Filtering and Functional Approximations, arXiv:1611.09293 ​, 2017
Keywords:
Bayesian Parameter Estimation via Filtering and Functional Approximations
  • C. Bayer, J Happola, R. Tempone, Implied Stopping Rules for American Basket Options from Markovian  Projection,  arXiv:1705.00558v1May 2017 
Keywords:
Implied Stopping Rules for American Basket Options from Markovian Projection
  • ​A. Haji-Ali, R. Tempone, "Multilevel and Multi-index Monte Carlo methods for the McKean-Vlasov equation", has been accepted for publication in Statistics and Computing. 2017
Keywords:
Multilevel and Multi-index Monte Carlo methods for the McKean-Vlasov equation
Refereed Journals
  • ​Litvinenko, Alexander, Marc Genton, Ying Sun, and David Keyes, "ℋ‐matrix techniques for approximating large covariance matrices and estimating its parameters", Proc. Appl. Math. Mech., 16 (2016): 731-732
Keywords:
ℋ‐matrix
Conference Proceedings
  • ​Chernov, Alexey, Haakon Hoel, Kody Law, Fabio Nobile, and Raúl Tempone, "Multilevel Ensemble Kalman filtering for spatially extended models", arXiv preprint 1608.08558, (2016)
Keywords:
Monte Carlo, multilevel, filtering, Kalman filter, ensemble Kalman filter
  • ​Hall, Eric Joseph, Håkon Hoel, Mattias Sandberg, Anders Szepessy, and Raúl Tempone, "Computable Error Estimates for Finite Element Approximations of Elliptic Partial Differential Equations with Rough Stochastic Data", SIAM Journal on Scientific Computing, Volume 38, no. 6 (2016): A3773-A3807
Keywords:
a posteriori error, Galerkin error, quadrature error, elliptic PDE, random PDE, Monte Carlo methods, lognormal
Refereed Journals
  • Hoel, Håkon, Juho Häppölä, and Raúl Tempone, "Construction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo", In: Cools R., Nuyens D. (eds) Monte Carlo and Quasi-Monte Carlo Methods. Springer Proceedings in Mathematics & Statistics, vol 163.
Keywords:
Multilevel monte carlo, Stochastic differential equations, Euler–Maruyama method, Adaptive methods, A posteriori error estimation, Adjoints
Conference Proceedings
  • N. Ben Rached, A. Kammoun, M.-S. Alouini, and R. Tempone, “An Exact Power Series Formula of the Outage Probability with Noise and Interference over Generalized Fading Channels”, IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’2016), Valencia, Spain, Sep. 2016​
Keywords:
moment-based approach, outage probability, cochannel interference, power series expansion, cross-moments, Rician fading environment, convergence study.
Conference Proceedings
  • C. BenIssaid, N. Ben Rached, A. Kammoun, M.-S. Alouini, and R. Tempone, “On the Sum of Gamma-Gamma Variates with Application to the Fast Outage Probability Evaluation over Fading Channels ”, IEEE GlobalSIP Symposium, Washington, DC, USA, Dec. 2016. ​​     
Keywords:
Gamma-Gamma, generalized-K, importance sampling, Monte Carlo, bounded relative error, outage probability, maximum ratio combining
Conference Proceedings
  • E. Kalligiannaki, A. Chazirakis, A. Tsourtis, M.A. Katsoulakis, P. Plechac, and V. Harmandaris, Parametrizing coarse grained models for molecular systems at equilibrium, EPJ ST, 225(8), 1347-1372, 2016, DOI: 10.1140/epjst/e2016-60145-x.
Keywords:
Parametrizing coarse grained models for molecular systems at equilibrium
Refereed Journals
  • ​ Soeren Wolfers, Fabio Nobile, Raul Tempone, Sparse approximation of multilinear problems with applications to kernel-based methods in UQ. Submitted arXiv 1609.00246, Sept 2016.
Keywords:
Sparse approximation of multilinear problems with applications to kernel-based methods in UQ
  • C. Bayer, M. Siebenmorgen, R. Tempone, Smoothing the payoff for efficient computation of Basket option prices,  arXiv:1607.05572, 2016​
Keywords:
Basket option pricing, smoothing payoff
  • R. Garra, E. Orsingher, M. Scavino, Some probabilistic properties of fractional point processes, Submitted arXiv:1604.05235, April 2016.
Keywords:
Fractional point processes, Bern?stein functions, Space-time Fractional Poisson processes, grey Brownian motion
  • LFR Espath, AF Sarmiento, P Vignal, BON Varga, AMA Cortes, L Dalcin, VM Calo, Energy Exchange Analysis in Droplet Dynamics via the Navier–Stokes–Cahn–Hilliard Model, Journal of Fluid Mechanics, Apr 2016.
Keywords:
Energy Exchange Analysis in Droplet Dynamics via the Navier–Stokes–Cahn–Hilliard Model
Refereed Journals
  • H. G. Matthies, E. Zander, B. V. Rosić, A. Litvinenko, O. Pajonk, Inverse Problems in a Bayesian Setting, Chapter in the book Computational Methods for Solids and Fluids, edited by Adnan Ibrahimbegovic, Springer, 2016
Keywords:
Inverse Problems, Bayesian Setting
  • H. Matthies, E. Zander, B. Rosic, A. Litvinenko​; Parameter Estimation via Conditional Expectation - A Bayesian Inversion, 2016
Keywords:
Parameter Estimation, Conditional Expectation, Bayesian Inversion
  • I. Babuska, Z. Sawlan, M. Scavino, B. Szabo, R. Tempone, Bayesian inference and model comparison for metallic fatigue data, Computer Methods in Applied Mechanics and Engineering, , Volume 304, 1 June 2016, Pages 171-196, ISSN 0045-7825​​​​
Keywords:
Metallic fatigue data; fatigue life prediction; random fatigue-limit models; maximum likelihood methods; Bayesian computational techniques for model calibration/ranking; predictive accuracy for Bayesian models.
Refereed Journals
  • C. Ben Hammouda, A. Moraes, R. Tempone, Multilevel hybrid split-step implicit tau-leap, Numerical Algorithms, pp 1-34, June 2016
Keywords:
Stochastic reaction networks, Multilevel Monte Carlo, Split-step implicit
Refereed Journals
  • A. Haji-Ali, F. Nobile, L. Tamellini, R. Tempone, Multi-index Stochastic Collocation convergence rates for random PDEs with parametric regularity. To appear in Foundations of Computational Mathematics. 2016
Keywords:
Multi-index Stochastic Collocation convergence rates for random PDEs with parametric regularity
Refereed Journals
  • A. Haji-Ali, F. Nobile, L. Tamellini, R. TemponeMulti-Index Stochastic Collocation for random PDEsComputer Methods in Applied Mechanics and Engineering​, 2016
Keywords:
Multi-Index Stochastic Collocation for random PDEs
Refereed Journals
  • F. Nobile, L. Tamellini, R. Tempone and F. Tesei, An adaptive sparse grid algorithm for elliptic PDEs with lognormal diffusion coefficient, “Sparse Grids and Applications - Stuttgart 2014”, Lecture Notes in Computational Science and Engineering, Volume 109 2016, Springer
Keywords:
An adaptive sparse grid algorithm with application to elliptic PDEs with lognormal diffusion coefficient
  • Gabriela Malenova, Mohammad Motamed, Olof Runborg, Raul Tempone, A Sparse Stochastic Collocation Technique for High Frequency Wave Propagation with Uncertaintyaccepted for publication in Journal on Uncertainty Quantification, May 2016
Keywords:
A Sparse Stochastic Collocation Technique for High Frequency Wave Propagation with Uncertainty
Refereed Journals
  • C. Bayer, A. Moraes, R. Tempone, P. Vilanova, An Efficient Forward-Reverse Expectation-Maximization Algorithm for Statistical Inference in Stochastic Reaction Networks, Stochastic Analysis and Applications, Volume 34, Issue 2, 2016
Keywords:
Forward-reverse algorithm, Monte Carlo EM algorithm, inference for stochastic reaction networks, bridges for continuous-time Markov chains.
Refereed Journals
  • Matteo Icardi, Gianluca Boccardo, Raul Tempone, On the predictivity of pore-scale simulations: estimating uncertainties with multilevel Monte Carlo, Advances in Water Resources, Feb. 2016
Keywords:
pore-scale simulation, multilevel Monte Carlo, stochastic upscaling, uncertainty quantification
Refereed Journals
  • Håkon Hoel, Kody J. H. Law, Raul Tempone, "Multilevel ensemble Kalman filtering", SIAM Journal on Numerical Analysis, Volume 54 no.3, (2016). 1813–1839
Keywords:
Multilevel ensemble Kalman filtering
Refereed Journals
  • F. Ruggeri, Z. Sawlan, M. Scavino, R. Tempone, A hierarchical Bayesian setting for an inverse problem in linear parabolic PDEs with noisy boundary conditions, accepted for publication in Bayesian Analysis, April 2016
Keywords:
linear parabolic PDEs, noisy boundary parameters, Bayesian inference, heat equation, thermal diffusivity
Refereed Journals
  • A. Moraes, R. Tempone, and P. Vilanova. A multilevel adaptive reaction-splitting simulation method for stochastic reaction networks. SIAM Journal on Scientific Computing (SISC), Vol 38, Issue 4, 2016.
Keywords:
Error estimates, error control, control variates, weak approximation, hybrid algorithms, multilevel Monte Carlo, Chernoff tau-leap, reaction splitting
Refereed Journals
  • A. Moraes, R. Tempone, P. Vilanova, Multilevel Hybrid Chernoff Tau-leap, BIT Numerical Mathematic, Volume 56, Issue 1pp 189–239​. March 2016. 
Keywords:
Error estimates, error control, control variates, weak approximation, hybrid algorithms, multilevel Monte Carlo, Chernoff tau-leap
Refereed Journals
  • J. E. Castrillon-Candas, F. Nobile, R. F. Tempone, Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations, ​Accepted for publication in Computers and Mathematics with Applications, Jan. 2016
Keywords:
Uncertainty Quantification, Stochastic Collocation, Stochastic PDEs, Finite Elements, Complex Analysis, Smolyak Sparse Grids.
Refereed Journals
  • N. Ben Rached, F. Benkhelifa, M.-S. Alouini, and R. Tempone, “A Fast Simulation Method for the Log-Normal Sum Distribution Using a Hazard Rate Twisting Technique”, IEEE International Conference on Communication (ICC'15), London, UK, Jun. 2015​
Keywords:
Log-normal sum distribution, Crude Monte Carlo, Rare events, Importance Sampling, Hazard rate twisting
Conference Proceedings
  • N. Ben Rached, A. Kammoun, M.-S. Alouini, and R. Tempone, “A Unified Simulation Approach for the Fast Outage Capacity Evaluation over Generalized Fading Channels”, IEEE International Symposium on Information Theory (ISIT'15), Hong Kong, Jun. 2015​
Keywords:
Outage capacity, fading channels, hazard rate twisting, Importance Sampling, asymptotic optimality
Conference Proceedings
  • A. Iania, Basket option pricing for processes with jumps using sparse grids and Fourier transforms Master Thesis, Politecnico di Torino - KAUST, 2015
Keywords:
Basket option pricing for processes with jumps using sparse grids and Fourier transforms
  • N. Ben Rached, A. Kammoun, M. Alouini, R. Tempone, Unified Importance Sampling Schemes for Efficient Simulation of Outage Capacity over Generalized Fading Channels, Accepted for publication in IEEE Journal of Selected Topics in Signal Processing, 2015
Keywords:
Outage capacity, naive Monte Carlo, hazard rate twisting, Importance Sampling, asymptotic optimality, bounded relative error
Refereed Journals
  • Eric Joseph Hall, Hakon Hoel, Mattias Sandberg, Anders Szepessy, Raul Tempone​, Computable error estimates for finite element approximations of elliptic partial  differential equations with rough stochastic data, Submitted arXiv Oct. 2015
Keywords:
Computable error estimates for finite element approximations of elliptic partial differential equations with rough stochastic data
  • Soumaya Elkantassi, Fourier Transform Methods for Option PricingGraduation Project Report​, Hosting Institution: KAUST, June 2015
Keywords:
Fourier Transform Methods for Option Pricing
  • G. Migliorati, F. Nobile, R. Tempone, Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations in random points, Journal of Multivariate Analysis, Vol. 142,  Pages 167–182. December 2015.​​​
Keywords:
approximation theory, discrete least squares, noisy evaluations, error analysis, convergence rates, large deviations, learning theory, multivariate polynomial approximation
Refereed Journals
  • Fabrizio Bisetti, Daesang Kim, Omar Knio, Quan Long, and Raul Tempone. Optimal Bayesian Experimental Design for Priors of Compact Support with Application to Shock-Tube Experiments for Combustion Kinetics.  Accepted by International Journal for Numerical Methods in Engineering​​
Keywords:
Bayesian optimal experimental design; Laplace approximation; Truncated Gaussian approximation; Polynomial surrogates; Shock–tube; Combustion kinetics
Refereed Journals
  • Nadhir Ben Rached, Abla Kammoun, Mohamed-Slim Alouini, and Raul Tempone, An Efficient Simulation Scheme of the Outage Probability with Co-Channel Interference, will be published in the Proceedings of IEEE  GLOBECOM 2015
Keywords:
Outage Probability, sum of correlated Lognormal, Importance Sampling, covariance matrix scaling, computational gain, naive Monte Carlo simulations.
Conference Proceedings
  • Yuxin Chen, David Keyes, Kody J.H. Law, Hatem Ltaief, Accelerated dimension-independent adaptive Metropolis, Submitted Jun 2015, arXiv:1506.05741
Keywords:
Accelerated dimension-independent adaptive Metropolis
  • N. Ben Rached, A. Kammoun, M.-S. Alouini, and R. Tempone, An Improved Hazard Rate Twisting Approach for the Statistic of the Sum of Subexponential Variates, Communications Letters, IEEE, Volume:19 Issue:1, 2015​
Keywords:
Hazard rate twisting, asymptotic optimality, minmax approach, subexponential, twisting parameter, variance reduction
Refereed Journals
  • Olivier Le Maitre, Omar Knio, and Alvaro Moraes, Variance Decomposition in Stochastic SimulatorsThe Journal of Chemical Physics, Volume 142, Issue 24, 2015
Keywords:
Variance Decomposition in Stochastic Simulators
Refereed Journals
  • Dishi Liu, Alexander Litvinenko, Claudia Schillings, and Volker Schulz, Quantification of airfoil geometry-induced aerodynamic uncertainties - comparison of approaches submitted 2015
Keywords:
Quantification of airfoil geometry-induced aerodynamic uncertainties - comparison of approaches
  • Raul Verma, Matteo Icardi, Masa Prodanovic, Validation of direct pore scale modeling approaches to wettability, submitted March 2015
Keywords:
Validation of direct pore scale modeling approaches to wettability
  • Alexandros Beskos, Ajay Jasra, Kody Law, Raul Tempone and Yan Zhou​, Multilevel Sequential Monte Carlo Samplers, submitted 2015​
Keywords:
Multilevel Monte Carlo, Sequential Monte Carlo, Bayesian Inverse Problems
  • Sergey Dolgov, Boris N. Khoromskij, Alexander Litvinenko, Hermann G. Matthies, Polynomial Chaos Expansion of random coefficients and the solution of stochastic partial differential equations in the Tenso​r Train formatsubmitted to SIAM Journal on Uncertainty Quantification, Volume 3, Issue 1, p. 1109–1135, Nov. 2015. DOI:10.1137/140972536​
Keywords:
uncertainty quantification, polynomial chaos expansion, Karhunen-Loeve expansion, stochastic Galerkin, tensor product methods, tensor train format, adaptive cross approximation, block cross
Refereed Journals
  • F. Crocce, J. Happola, J. Kiessling, R. Tempone, Error analysis in Fourier methods for option pricing, Accepted for publication in the Journal of Computational Finance (JCF), Dec. 2015​
Keywords:
Error analysis, Option pricing, Fourier methods, Spectral methods, Levy processes, Stochastic processes, Hardy functions, Trapezoidal quadrature
Refereed Journals
  • B. Djehiche, H. Tembine, R. Tempone, A Stochastic Maximum Principle for Risk-Sensitive Mean-Field-Type Control, To appear in IEEE Transactions on Automatic Control, VOL. 60, NO. 10, October 2015. 
Keywords:
Optimization and Control (math.OC); Systems and Control (cs.SY); Probability (math.PR); Risk Management (q-fin.RM)
Refereed Journals
  • S. Aseeri, O. Batrašev, M. Icardi, B. Leu, A. Liu, N. Li, B.K. Muite, E. Müller, B. Palen, M. Quell, H. Servat, P. Sheth, R. Speck, M. Van Moer, J. Vienne, Solving the Klein-Gordon equation using Fourier spectral methods: A benchmark test for computer performance, submited to arXiv:1501.04552, 2015​​
Keywords:
HPC, and Fourier Methods
  • F. Nobile, L. Tamellini, R. Tempone, Comparison of Clenshaw–Curtis and Leja quasi-optimal sparse grids for the approximation of random PDEs, International Conference on Spectral and High-Order Methods 2014 (ICOSAHOM'14), Salt Lake City, Utah, USA, June 23-27, 2014. Spectral and High Order Methods for Partial Differential Equations. Volume 106 of the series Lecture Notes in Computational Science and Engineering, pp 475-482. Springer, 2015​​
Keywords:
Uncertainty Quantification ; PDEs with random data ; linear elliptic equations ; Stochastic Collocation methods ; Sparse grids approximation ; Leja points ; Clenshaw–Curtis points
  • A. Haji-Ali, F. Nobile, R. Tempone​, Multi Index Monte Carlo: When Sparsity Meets Sampling, Numerische Mathematik, Vol. 132, Pages  767–806, 2016.​​​
Keywords:
Multilevel Monte Carlo, Monte Carlo, Partial Differential Equations with random data, Stochastic Differential Equations, Weak Approximation, Sparse Approximation, Combination Technique.
Refereed Journals
  • Q. Long, M. Motamed, R. Tempone, Fast Bayesian optimal experimental design for seismic source inversion, Computer Methods in Applied Mechanics and Engineering, vol. 291, pp. 123-145, 2015.​​
Keywords:
Bayesian experimental design, Information gain, Laplace approximation, Monte Carlo sampling, Seismic source inversion, Sparse quadrature, Uncertainty quantification
Refereed Journals
  • A. Haji-Ali, F. Nobile, E. von Schwerin, R. Tempone​, Optimization of mesh hierarchies in Multilevel Monte Carlo samplersStochastic Partial Differential Equations: Analysis and Computations, Vol. 4, Issue 1, Pages  76–112, 2016.​​
Keywords:
Multilevel Monte Carlo, Monte Carlo, Partial Di erential Equations with random data, Stochastic Differential Equations, Optimal discretization
Refereed Journals
  • M. Motamed, F. Nobile, R. Tempone, Analysis and Computation of Hyperbolic PDEs with Random Data, Encyclopedia of Applied and Computational Mathematics, pp 51-58, November 2015
Keywords:
Analysis and Computation of Hyperbolic PDEs with Random Data
  • M. Motamed, F. Nobile, R. Tempone,  Analysis and computation of the elastic wave equation with random coefficients, Computers and Mathematics with Applications, Vol. 70, Issue 10, pp. 2454–2473, November 2015.
Keywords:
uncertainty quantification; stochastic partial differential equations; elastic wave equation; regularity; collocation method; error analysis.
Refereed Journals
  • J. Karlsson, S. Larsson, M. Sandberg, A. Szepessy, R. Tempone, An a posteriori error estimate for symplectic Euler approximation of optimal control problems, SIAM J. Sci. Comput. 37 (2015), A946-A969. [doi:10.1137/140959481]. 
Keywords:
Optimal Control, Error Estimates, Adaptivity, Error Control
Refereed Journals
  • F. Nobile, L. Tamellini, R. Tempone, Convergence of quasi-optimal sparse grid approximation of Hilbert-valued functions: application to random elliptic PDEs, To appear in Numerische Mathematik, pp. 1—46, 2015. DOI 10.1007/s00211-015-0773-y. 
Keywords:
Uncertainty Quantification · random PDEs · linear elliptic equations · multivariate polynomial approximation · best M-terms polynomial approximation · Smolyak approximation · Sparse grids · Stochastic Collocation method
Refereed Journals
  • N. Collier, A. Haji-Ali, F. Nobile, E. von Schwerin, R. TemponeA Continuation Multilevel Monte Carlo algorithmBIT Numerical Mathematics, Volume 55, Issue 2, pp 399-432, June 2015
Keywords:
SDEs, SPDEs, Multilevel Monte Carlo, Numerical Analysis
Refereed Journals
  • A. Chkifa, A. Cohen, G. Migliorati, F. Nobile, R. Tempone, Discrete least squares polynomial approximation with random evaluations - application to parametric and stochastic elliptic PDEs, ESAIM: Mathematical Modelling and Numerical Analysis, 49 (3):815-837, 2015.
Keywords:
approximation theory, polynomial approximation, least squares, parametric and stochastic PDEs, high-dimensional approximation
Refereed Journals
  • Q. Long, M. Scavino, R. Tempone, S. Wang. A Laplace method for under-determined Bayesian optimal experimental designs, Computer Methods in Applied Mechanics and Engineering​, Volum​e 285, Pages 849–876, March 2015.​
Keywords:
Bayesian statistics
Refereed Journals
  • Nadhir Ben Rached, Fatma Benkhelifa, Abla Kammoun, Mohamed-Slim Alouini, Raul Tempone, A Fast Simulation Method for the Sum of Subexponential Distributions, submitted to arXiv:1406.4689v4, Jun. 2014
Keywords:
A Fast Simulation Method for the Sum of Subexponential Distributions
  • Kody J.H. Law, Hamidou Tembine, Raul Tempone, Deterministic Methods for Nonlinear Filtering, part I: Mean-field Ensemble Kalman Filtering, submitted to arXiv:1409.0628v2, Nov. 2014
Keywords:
Deterministic Methods for Nonlinear Filtering, part I: Mean-field Ensemble Kalman Filtering
  • K.J.H. Law, D. Sanz-Alonso, A. Shukla, A.M. StuartControlling Unpredictability with Observations in the Partially Observed Lorenz '96 Modelsubmited to arXiv:1411.3113v1, Nov. 2014.
Keywords:
Controlling Unpredictability with Observations in the Partially Observed Lorenz '96 Model
  • Tiangang CuiKody J.H. LawYoussef M. Marzouk, Dimension-independent likelihood-informed MCMCsubmited to  arXiv:1411​.3688v1, Nov. 2014
Keywords:
Dimension-independent likelihood-informed MCMC
  • Nathan Quadrio, "Multilevel Monte Carlo method for PDEs with fluid dynamic applications", Master Thesis, KAUST, October 2014.
Keywords:
Uncertainty Quantification, Monte Carlo Sampling, Variance Reduction, Multi- level Monte Carlo
  • Nadhir Ben Rached, Fatma Benkhelifa, Abla Kammoun, Mohamed-Slim Alouini, and Raul Tempone, "Additional Results on the Hazard Rate Twisting-Based Simulation Approach", submitted to IEEE, 2014
Keywords:
Crude Monte Carlo, rare events, Importance Sampling, hazard rate twisting, asymptotically optimal, twisting parameter.
  • Matteo Icardi, Gianluca Boccardo, Daniele L. Marchisio, Tiziana Tosco, and Rajandrea Sethi, Pore-scale simulation of fluid flow and solute dispersion in three-dimensional porous media. Phys. Rev. E., 90 , 2014
Keywords:
Pore-scale simulation of fluid flow and solute dispersion in three-dimensional porous media
Refereed Journals
  • Hakon Hoel, Juho Happola, and Raul Tempone, Construction of a mean square error adaptive Euler–Maruyama method with applications in multilevel Monte Carlo. 2014​​​
Keywords:
Adaptive time stepping, stochastic differential equations, multilevel Monte Carlo.
  • Bilal Saad and Mazen Saad, "A combined finite volume–nonconforming finite element scheme for compressible two phase flow in porous media", Numerische Mathematik, Springer-Verlag Berlin Heidelberg 2014
Keywords:
Two-phase flow in porous medium, finite volume methods, finite element methods, convergence study
Refereed Journals
  • Annunziato, M. , Borzì, A. , Nobile, F. and Tempone, R., On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks. Applied Mathematics, Vol.5 No.16, September 2014. DOI: 10.4236/am.2014.516239
Keywords:
Hamilton-Jacobi-Bellman Equation, Fokker-Planck Equation, Optimal Control Theory, Stochastic Differential Equations, Hybrid Systems
Refereed Journals
  • L. Selvakumaran, Q. Long, S. Prudhomme, G. Lubineau, On the detectability of transverse cracks in laminated composites using electrical potential change measurements, Composite Structures, 121, 237-246 (2014).​
Keywords:
Transverse cracking, Sensitivity, Impedance tomography, Analytical model, Laminated composites
Refereed Journals
  • Hakon Hoel and Henrik Nyberg, "An Extension of Clarke’s Model With Stochastic Amplitude Flip Processes", IEEE Transactions on Communications, 2014.
Keywords:
Multipath channels, Gaussian processes, Ray tracing.