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 Teor. Veroyatnost. i Primenen., 1961, Volume 6, Issue 1, Pages 47–56 (Mi tvp4747)

Construction of Non-Homogeneous Markov Processes by Means of a Random Substitution of Time

V. A. Volkonskii

Moscow

Abstract: It is proved that a continuous single-dimensional Markov process $y(t)$ with wide restrictions can be obtained from the Wiener process $x(t)$ in the following form: $y(t)=\psi[x(\tau_t),t]$, where $\psi(x,t)$ is a continuous function, monotonic in $x$ for a given $t$, and $\tau _t$ is a non-decreasing random function of $t$ (Theorem 1).
Conditions are given which should be met by the Markov process $x(t)$ in abstract space and the random function $\tau_t$ so that the process $y(t)=x(\tau_t)$ will also be a Markov process (Theorem 2).

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English version:
Theory of Probability and its Applications, 1961, 6:1, 42–51

Citation: V. A. Volkonskii, “Construction of Non-Homogeneous Markov Processes by Means of a Random Substitution of Time”, Teor. Veroyatnost. i Primenen., 6:1 (1961), 47–56; Theory Probab. Appl., 6:1 (1961), 42–51

Citation in format AMSBIB
\Bibitem{Vol61} \by V.~A.~Volkonskii \paper Construction of Non-Homogeneous Markov Processes by Means of a Random Substitution of Time \jour Teor. Veroyatnost. i Primenen. \yr 1961 \vol 6 \issue 1 \pages 47--56 \mathnet{http://mi.mathnet.ru/tvp4747} \transl \jour Theory Probab. Appl. \yr 1961 \vol 6 \issue 1 \pages 42--51 \crossref{https://doi.org/10.1137/1106003} 

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This publication is cited in the following articles:
1. I. V. Evstigneev, “Stochastic extremal problems and the strong Markov property of random fields”, Russian Math. Surveys, 43:2 (1988), 1–49