Comparison of Markov processes via infinitesimal generators

We derive comparison results for Markov processes with respect to stochastic orderings induced by function classes. Our main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators implies ordering of the processes. Unlike in previous work no boundedness assumptions on the function classes are needed anymore. We also present an integral version of the comparison result which does not need the local comparability assumption of the generators. The method of proof is also used to derive comparison results for time-discrete Markov processes.