Comparison results for Markov processes with respect to function-class-induced (integral) stochastic orders have a long history. The most general results so far for this problem have been obtained based on the theory of evolution systems on Banach spaces. In this paper we transfer the martingale comparison method, known for the comparison of semimartingales to Markovian semimartingales, to general Markov processes. The basic step of this martingale approach is the derivation of the supermartingale property of the linking process, giving a link between the processes to be compared. This property is achieved using the characterization of Markov processes by the associated martingale problem in an essential way. As a result, the martingale comparison method gives a comparison result for Markov processes under a general alternative but related set of regularity conditions compared to the evolution system approach.

中文翻译：

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马尔可夫过程的鞅比较法

马尔可夫过程关于函数类诱导（积分）随机顺序的比较结果由来已久。迄今为止，该问题最普遍的结果是基于 Banach 空间上的进化系统理论获得的。在本文中，我们将用于比较半鞅与马尔可夫半鞅的鞅比较方法转移到一般马尔可夫过程。这种鞅方法的基本步骤是推导链接过程的超鞅性质，给出要比较的过程之间的链接。该属性是通过相关的鞅问题以一种基本的方式使用马尔可夫过程的表征来实现的。因此，