A coupling technique for stochastic comparison of functions of Markov processes

The aim of this work is to obtain explicit conditions (i.e., conditions on the transition rates) for the stochastic comparison of Markov Processes. A general coupling technique is used to obtain necessary and sufficient conditions for the construction of a coupling Markov Process which stays in a fixed set K for all times and with given marginal processes. The strong stochastic comparison – or, more generally, the stochastic comparison through states functions – appears as a particular case. An example in the Reliability Theory is developed and proves the efficiency of the method. Systems with multiple component types and redundant units are stochastically compared directly or through particular functions.