The parallel replica method for simulating long trajectories of Markov chains

Abstract

The parallel replica dynamics, originally developed by A.F. Voter, efficiently simulates very long trajectories of metastable Langevin dynamics. We present an analogous algorithm for discrete time Markov processes. Such Markov processes naturally arise, for example, from the time discretization of a continuous time stochastic dynamics. Appealing to properties of quasistationary distributions, we show that our algorithm reproduces exactly (in some limiting regime) the law of the original trajectory, coarsened over the metastable states.

13 pages, 6 figures

References in corpus (1)

• A Generalized Parallel Replica Dynamics

Cited by in corpus (6)

• A Generalized Parallel Replica Dynamics
• Accelerated dynamics: Mathematical foundations and algorithmic improvements
• gen.parRep: a first implementation of the Generalized Parallel Replica dynamics for the long time simulation of metastable biochemical systems
• Parallel replica dynamics method for bistable stochastic reaction networks: simulation and sensitivity analysis
• Stationary averaging for multi-scale continuous time Markov chains using parallel replica dynamics
• Generalizing Parallel Replica Dynamics: Trajectory Fragments, Asynchronous Computing, and PDMPs