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Russia Yekaterinburg
Year
2021
Volume
31
Issue
4
Pages
536-561
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Section Mathematics
Title Approximation of value function of differential game with minimal cost
Author(-s) Averboukh Yu.V.ab
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
Abstract The paper is concerned with the approximation of the value function of the zero-sum differential game with the minimal cost, i.e., the differential game with the payoff functional determined by the minimization of some quantity along the trajectory by the solutions of continuous-time stochastic games with the stopping governed by one player. Notice that the value function of the auxiliary continuous-time stochastic game is described by the Isaacs–Bellman equation with additional inequality constraints. The Isaacs–Bellman equation is a parabolic PDE for the case of stochastic differential game and it takes a form of system of ODEs for the case of continuous-time Markov game. The approximation developed in the paper is based on the concept of the stochastic guide first proposed by Krasovskii and Kotelnikova.
Keywords differential games with minimal cost, stochastic guide, approximation of the value function, Isaacs-Bellman equation
UDC 517.977.8
MSC 49N70, 91A23, 91A25
DOI 10.35634/vm210402
Received 5 July 2021
Language English
Citation Averboukh Yu.V. Approximation of value function of differential game with minimal cost, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 4, pp. 536-561.
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