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

Author

Listed:
  • Karlsson Jesper
  • Tempone Raúl

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

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.

Suggested Citation

  • Karlsson Jesper & Tempone Raúl, 2011. "Towards automatic global error control: Computable weak error expansion for the tau-leap method," Monte Carlo Methods and Applications, De Gruyter, vol. 17(3), pages 233-278, January.
    • Handle: RePEc:bpj:mcmeap:v:17:y:2011:i:3:p:233-278:n:3
    DOI: 10.1515/mcma.2011.011
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