Mathematics – Numerical Analysis
Scientific paper
2010-04-17
Monte Carlo Methods and Applications 2011 17:3, 233-278
Mathematics
Numerical Analysis
Scientific paper
10.1515/MCMA.2011.011
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 algorithm. 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.
Karlsson Jesper
Tempone Raul
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