Kolmogorov's Equations for Jump Markov Processes and their Applications\n to Control Problems

2021/09/10 by Eugene A. Feinberg, Feinberg, Eugene A., Albert N. Shiryaev +1 · 1 citation
Economics, Econometrics and Finance · Earth and Planetary Sciences · Computer Science · #Stochastic processes and financial applications #Aquatic and Environmental Studies #Mathematical Control Systems and Analysis

paper · pdf · doi:10.48550/arxiv.2109.05079

Abstract

This paper describes the structure of solutions to Kolmogorov's equations for\nnonhomogeneous jump Markov processes and applications of these results to\ncontrol of jump stochastic systems. These equations were studied by Feller\n(1940), who clarified in 1945 in the errata to that paper that some of its\nresults covered only nonexplosive Markov processes. In this work, which is\nlargely of a survey nature, the case of explosive processes is also considered.\nThis paper is based on the invited talk presented by the authors at the\nconference "Chebyshev-200", and it describes the results of their joined\nstudies with Manasa Mandava (1984-2019).\n

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