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

 Teor. Veroyatnost. i Primenen., 1968, Volume 13, Issue 2, Pages 362–365 (Mi tvp858)

Short Communications

On the optimal control by means of a random time substitution in a continuous Markov process

A. Ya. Kogan

Moscow

Abstract: Let $X$ be a homogeneous Markov Feller process with continuous paths in a compact $E$. For the process $X^u$ obtained from $X$ by means of a random time substitution connected with the additive functional (1), we prove the existence of a continuous optimal control $u^*(x)$ (4) that minimizes the risk $R^u(x)$ (2). Further, we show that the optimal risk $R^*(x)$ is the only continuous solution of the equation (3), where $A$ is the weak infinitesimal operator of $X$. Under some assumptions we obtain an equation for a lower bound $r(x)$ of the optimal risk $R^*(x)$.

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English version:
Theory of Probability and its Applications, 1968, 13:2, 343–345

Bibliographic databases:

Citation: A. Ya. Kogan, “On the optimal control by means of a random time substitution in a continuous Markov process”, Teor. Veroyatnost. i Primenen., 13:2 (1968), 362–365; Theory Probab. Appl., 13:2 (1968), 343–345

Citation in format AMSBIB
\Bibitem{Kog68} \by A.~Ya.~Kogan \paper On the optimal control by means of a~random time substitution in a~continuous Markov process \jour Teor. Veroyatnost. i Primenen. \yr 1968 \vol 13 \issue 2 \pages 362--365 \mathnet{http://mi.mathnet.ru/tvp858} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=255280} \zmath{https://zbmath.org/?q=an:0181.44802|0167.17002} \transl \jour Theory Probab. Appl. \yr 1968 \vol 13 \issue 2 \pages 343--345 \crossref{https://doi.org/10.1137/1113044} 

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This publication is cited in the following articles:
1. N. V. Krylov, “Control of Markov processes and $W$-spaces”, Math. USSR-Izv., 5:1 (1971), 233–266
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