Comparison of time-inhomogeneous Markov processes
Comparison of time-inhomogeneous Markov processes
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DOI：
10.1017/apr.2016.63
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发表时间：
2015-05
影响因子：
1.2
通讯作者：
Ludger Rueschendorf;Alexander Schnurr;V. Wolf
中科院分区：
文献类型：
--
作者：
Ludger Rueschendorf;Alexander Schnurr;V. Wolf
摘要给出了非时齐马氏过程关于具有诱导随机序的函数类的比较结果。主要结果表明，两个过程的比较，只要它们的无穷小生成元的可比性以及一个过程的不变性的性质是假设的。相应的证明是基于Banach空间中的非齐次演化问题的解的一个表示结果，它扩展了文献中的已知结果。在此基础上，建立了由有界函数类和无界函数类诱导的马氏过程的一个排序结果。我们给各种应用程序的时间非齐次扩散，独立增量的过程，和列维驱动的扩散过程。
Abstract Comparison results are given for time-inhomogeneous Markov processes with respect to function classes with induced stochastic orderings. The main result states the comparison of two processes, provided that the comparability of their infinitesimal generators as well as an invariance property of one process is assumed. The corresponding proof is based on a representation result for the solutions of inhomogeneous evolution problems in Banach spaces, which extends previously known results from the literature. Based on this representation, an ordering result for Markov processes induced by bounded and unbounded function classes is established. We give various applications to time-inhomogeneous diffusions, to processes with independent increments, and to Lévy-driven diffusion processes.