A New Method for Coupling Random Fields

Abstract

Given a Markov chain, a stochastic flow that simultaneously constructs sample paths started at each possible initial value can be constructed as a composition of random fields. Here, a method is described for coupling flows by modifying an arbitrary field (consistent with the Markov chain of interest) by an independence MetropolisHastings iteration. The resulting stochastic flow is shown to have many desirable coalescence properties, regardless of the form of the original flow.