Kolmogorov's Equations for Jump Markov Processes and Their Applications to Control Problems

IF 0.5 4区 数学 Q4 STATISTICS & PROBABILITY Theory of Probability and its Applications Pub Date : 2021-09-10 DOI:10.1137/s0040585x97t990630
E. Feinberg, A. Shiryaev
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Abstract

This paper describes the structure of solutions to Kolmogorov’s equations for nonhomogeneous jump Markov processes and applications of these results to control of jump stochastic systems. These equations were studied by Feller (1940), who clarified in 1945 in the errata to that paper that some of its results covered only nonexplosive Markov processes. In this work, which is largely of a survey nature, the case of explosive processes is also considered. This paper is based on the invited talk presented by the authors at the conference “Chebyshev-200”, and it describes the results of their joined studies with Manasa Mandava (1984-2019).
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跳跃马尔可夫过程的Kolmogorov方程及其在控制问题中的应用
本文讨论了非齐次跳变马尔可夫过程的Kolmogorov方程解的结构及其在跳变随机系统控制中的应用。Feller(1940)对这些方程进行了研究,他在1945年对那篇论文的勘误表中澄清说,他的一些结果只涵盖了非爆炸马尔可夫过程。在这项主要是调查性质的工作中,也考虑了爆炸过程的情况。本文基于作者在“chebyhev -200”会议上的邀请演讲,并描述了他们与Manasa Mandava(1984-2019)联合研究的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Theory of Probability and its Applications
Theory of Probability and its Applications 数学-统计学与概率论
CiteScore
1.00
自引率
16.70%
发文量
54
审稿时长
6 months
期刊介绍: Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.
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