A coupling technique for stochastic comparison of functions of Markov processes (Q1568374)

The basic framework is two continuous-time Markov jump processes with (countable) state spaces \(E\) and \(F\) and functions \(\varphi\) and \(\psi\) from these into an ordered set \(G\). This is a natural generalization of the situation when each state has an associated cost (which defines a function from the state space to the nonnegative reals). The ordering on \(G\) allows a stochastic comparison of the two Markov processes to be defined; roughly, this is that, on \(G\), one process is below the other in distribution. Such a relationship between processes turns out to be equivalent to the existence of a suitable coupling Markov process with values in \(E \times F\). Explicit conditions, in terms of transition rates, for this coupling to exist are given. An example from reliability illustrates the usefulness of the results.