The parallel replica method for computing equilibrium averages of Markov chains
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David Aristoff
Abstract
An algorithm is proposed for computing equilibrium averages of Markov chains which suffer from metastability – the tendency to remain in one or more subsets of state space for long time intervals. The algorithm, called the parallel replica method (or ParRep), uses many parallel processors to explore these subsets more efficiently. Numerical simulations on a simple model demonstrate consistency of the method. A proof of consistency is given in an idealized setting. The parallel replica method can be considered a generalization of A. F. Voter's parallel replica dynamics, originally developed to efficiently simulate metastable Langevin stochastic dynamics.
Funding source: National Science Foundation
Award Identifier / Grant number: NSF-DMS-1522398
The author acknowledges Gideon Simpson (Drexel University), Tony Lelièvre (École des Ponts ParisTech) and Lawrence Gray (University of Minnesota) for fruitful discussions.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- The parallel replica method for computing equilibrium averages of Markov chains
- Mathematical verification of the Monte Carlo maximum cross-section technique
- Infinite-dimensional Monte-Carlo integration
- Widening and clustering techniques allowing the use of monotone CFTP algorithm
- Constructing positivity preserving numerical schemes for the two-factor CIR model
- Simulation of random variates with the Morgenstern distribution
Articles in the same Issue
- Frontmatter
- The parallel replica method for computing equilibrium averages of Markov chains
- Mathematical verification of the Monte Carlo maximum cross-section technique
- Infinite-dimensional Monte-Carlo integration
- Widening and clustering techniques allowing the use of monotone CFTP algorithm
- Constructing positivity preserving numerical schemes for the two-factor CIR model
- Simulation of random variates with the Morgenstern distribution
