{"title":"Kolmogorov's Equations for Jump Markov Processes and Their Applications to Control Problems","authors":"E. Feinberg, A. Shiryaev","doi":"10.1137/s0040585x97t990630","DOIUrl":null,"url":null,"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).","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"38 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and its Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/s0040585x97t990630","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
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).
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.