E. A. Feinberg, A. N. Shiryaev, “Kolmogorov's equations for jump Markov processes and their applications to control problems”, Teor. Veroyatnost. i Primenen., 2021, Volume 66, Issue 4,Pages <nobr>734

This article is cited in 4 papers

Kolmogorov's equations for jump Markov processes and their applications to control problems

E. A. Feinberg^a, A. N. Shiryaev^b

^a Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY, USA
^b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

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 [Trans. Amer. Math. Soc., 48 (1940), pp. 488–515], 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 “P. L. Chebyshev – 200,” and it describes the results of their joint studies with Manasa Mandava (1984–2019).

Keywords: Kolmogorov's equations, jump Markov processes, optimal control.

Received: 18.06.2021
Accepted: 18.06.2021

DOI: 10.4213/tvp5524