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

Karlsson Jesper () and Tempone Raúl ()
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Karlsson Jesper: Mathematical and Computer Sciences and Engineering (MCSE), King Abdullah University of Science and Technology (KAUST), Saudi Arabia.
Tempone Raúl: Mathematical and Computer Sciences and Engineering (MCSE), King Abdullah University of Science and Technology (KAUST), Saudi Arabia.

Monte Carlo Methods and Applications, 2011, vol. 17, issue 3, 233-278

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 (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:17:y:2011:i:3:p:233-278:n:3

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DOI: 10.1515/mcma.2011.011

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