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Monte Carlo Methods and Applications

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

1Mathematical and Computer Sciences and Engineering (MCSE), King Abdullah University of Science and Technology (KAUST), Saudi Arabia.

Citation Information: Monte Carlo Methods and Applications. Volume 17, Issue 3, Pages 233–278, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: 10.1515/mcma.2011.011, October 2011

Publication History

Received:
2010-05-25
Revised:
2011-07-26
Published Online:
2011-10-19

Abstract

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.

Keywords.: Tau-leap; weak approximation; reaction networks; Markov chain; error estimation; a posteriori error estimates; backward dual functions

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