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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1976, Volume 21, Issue 1, Pages 164–169 (Mi tvp3305)

Short Communications

Construction of the cost and optimal policies in a game problem of stopping of a Markov process

N. V. Elbakidze

Institute of Economics and Law of Academy of Sciences of GSSR, Tbilisi

Abstract: A minimax version of optimal stopping of a Markov process $\{x_n,\mathscr F_n,\mathbf P_x\}$, $n\ge 0$, with a phase space $(E,\mathscr B)$ (a game of two persons with opposite interests) is considered. The process $x_n$ can be stopped at any moment $n\ge 0$. If it is stopped by the first, second or both of the players, the first one gets, correspondingly, a reward $g(x_n)$, $G(x_n)$ or $e(x_n)$. If the process is not stopped, the first player gets reward $\displaystyle\varliminf_{n\to\infty}C(x_n)$. A recurrent procedure of constructing the cost and structure of optimal and $\varepsilon$-optimal stopping times is investigated.

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English version:
Theory of Probability and its Applications, 1976, 21:1, 163–168

Bibliographic databases:

Citation: N. V. Elbakidze, “Construction of the cost and optimal policies in a game problem of stopping of a Markov process”, Teor. Veroyatnost. i Primenen., 21:1 (1976), 164–169; Theory Probab. Appl., 21:1 (1976), 163–168

Citation in format AMSBIB
\Bibitem{Elb76} \by N.~V.~Elbakidze \paper Construction of the cost and optimal policies in a~game problem of stopping of a~Markov process \jour Teor. Veroyatnost. i Primenen. \yr 1976 \vol 21 \issue 1 \pages 164--169 \mathnet{http://mi.mathnet.ru/tvp3305} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=410903} \zmath{https://zbmath.org/?q=an:0366.60064} \transl \jour Theory Probab. Appl. \yr 1976 \vol 21 \issue 1 \pages 163--168 \crossref{https://doi.org/10.1137/1121016} 

• http://mi.mathnet.ru/eng/tvp3305
• http://mi.mathnet.ru/eng/tvp/v21/i1/p164

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Theory Probab. Appl., 53:3 (2009), 558–571
2. Attard N., “Nonzero-Sum Games of Optimal Stopping For Markov Processes”, Appl. Math. Optim., 77:3 (2018), 567–597