Comparison of Markov processes via infinitesimal generators
نویسنده
چکیده
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. In particular we apply this integral version to compare Markov processes and its speeding-down versions w.r.t. the supermodular order.
منابع مشابه
On a comparison result for Markov processes
A comparison theorem is stated for Markov processes in polish state spaces. We consider a general class of stochastic orderings induced by a cone of real functions. The main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators imply ordering of the processes. Several applications to convex type and to dependence orderings are given. In part...
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