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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board Member: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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CiteScore 2016: 0.70

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1569-3961
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Volume 17, Issue 3 (Jan 2011)

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

Jesper Karlsson
  • Mathematical and Computer Sciences and Engineering (MCSE), King Abdullah University of Science and Technology (KAUST), Saudi Arabia.
  • Email:
/ Raúl Tempone
  • Mathematical and Computer Sciences and Engineering (MCSE), King Abdullah University of Science and Technology (KAUST), Saudi Arabia.
  • Email:
Published Online: 2011-10-19 | DOI: https://doi.org/10.1515/mcma.2011.011

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

About the article

Received: 2010-05-25

Revised: 2011-07-26

Published Online: 2011-10-19

Published in Print: 2011-09-01



Citation Information: Monte Carlo Methods and Applications, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma.2011.011. Export Citation

Citing Articles

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[1]
Muruhan Rathinam
SIAM Journal on Numerical Analysis, 2016, Volume 54, Number 1, Page 415
[2]
Alvaro Moraes, Raúl Tempone, and Pedro Vilanova
BIT Numerical Mathematics, 2015
[3]
Alvaro Moraes, Raul Tempone, and Pedro Vilanova
Multiscale Modeling & Simulation, 2014, Volume 12, Number 2, Page 581

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