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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. SuchMarkov processes naturally arise, for example, from the time discretization ofa continuous time stochastic dynamics. Appealing to properties ofquasistationary distributions, we show that our algorithm reproduces exactly(in some limiting regime) the law of the original trajectory, coarsened overthe metastable states.

The parallel replica method for simulating long trajectories of Markov chains