Stationary averaging for multiscale continuous time markov chains using parallel replica dynamics

Ting Wang, Petr Plechac, David Aristiff

Abstract:

We propose two algorithms for simulating continuous time Markov chains in the
presence of metastability. We show that the algorithms correctly estimate, under the ergodicity
assumption, stationary averages of the process. Both algorithms, based on the idea of the parallel
replica method, use parallel computing in order to explore metastable sets more efficiently. The
algorithms require no assumptions on the Markov chains beyond ergodicity and the presence of identifiable metastability. In particular, there is no assumption on reversibility. For simpler illustration
of the algorithms, we assume that a synchronous architecture is used throughout of the paper. We
present error analyses, as well as numerical simulations on multi-scale stochastic reaction network
models in order to demonstrate consistency of the method and its efficiency.