Stochastic domination and Markovian couplings

Abstract

For continuous-time Markov chains with semigroups\nP, P' taking values in a partially ordered set, such that\nP ≤ <sub>st</sub> P', we show the existence of an order-preserving\nMarkovian coupling and give a way to construct it. From\nour proof, we also obtain the conditions of Brandt and Last for\nstochastic domination in terms of the associated intensity\nmatrices. Our result is applied to get necessary and sufficient\nconditions for the existence of Markovian\ncouplings between two Jackson networks.