Stochastic comparisons and couplings for interacting particle systems (Q1807924)

Consider two interacting particle systems with countable number of particles taking values in a partially ordered set. It is shown that the existence of the increasing Markovian coupling for these systems is equivalent to their stochastic ordering [a corresponding problem was posed by \textit{F. Forbes} and \textit{O. François}, ibid. 33, No. 3, 309-320 (1997; Zbl 0904.60076)]. Explicit construction of the coupling is given. The theory of network flows is essentially used in the proof of the main result.