Towards automatic global error control: computable weak error expansion for the tau-leap method

Towards automatic global error control: computable weak error expansion for the tau-leap method

Karlsson, Jesper; Tempone, Raúl " Towards automatic global error control: computable weak error expansion for the tau-leap method." Monte Carlo Methods Appl. 17 (2011), no. 3, 233–278.

Karlsson, Jesper; Tempone, Raúl
Tau-leap; weak approximation; reaction networks; Markov chain; error estimation; a posteriori error estimates; backward dual functions
2011
This work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error approximations are the basis for adaptive algorithms, a fundamental tool for numerical simulation of both deterministic and stochastic dynamical systems. These pure jump processes are simulated either by the tau-leap method, or by exact simulation, also referred to as dynamic Monte Carlo, the Gillespie Algorithm or the Stochastic Simulation Slgorithm. Two types of estimates are presented: an a priori estimate for the relative error that gives a comparison between the work for the two methods depending on the propensity regime, and an a posteriori estimate with computable leading order term.
ISSN (Print) 0929-9629