The parallel replica method for simulating long trajectories of Markov chains

David Aristoff 1 Tony Lelièvre 2, 3 Gideon Simpson 4
3 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : The parallel replica dynamics method, originally developed by A.F. Voter, can efficiently simulate very long trajectories of Langevin dynamics in the presence of metastability. In this work, we extend the algorithm to discrete in time Markov processes. We give a mathematical analysis of the algorithm which relies on the properties of quasistationary distributions. One application of the algorithm is the correction of time step discretization errors for the original parallel replica dynamics applied to Langevin dynamics.
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https://hal.archives-ouvertes.fr/hal-00934516
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Submitted on : Wednesday, January 22, 2014 - 11:03:13 AM
Last modification on : Friday, June 28, 2019 - 1:40:04 PM

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David Aristoff, Tony Lelièvre, Gideon Simpson. The parallel replica method for simulating long trajectories of Markov chains. Applied Mathematics Research eXpress, Oxford University Press (OUP): Policy H - Oxford Open Option A, 2014, 2, pp.332-352. ⟨10.1093/amrx/abu005⟩. ⟨hal-00934516⟩

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