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Teor. Veroyatnost. i Primenen., 1976, Volume 21, Issue 1, Pages 143–146 (Mi tvp3301)  

Short Communications

On events connected with reaching a set by sample paths of a stochastic process

M. I. Taksar

Moscow

Abstract: Let $\Gamma$ be a subset in the state space of a stochastic process $x_t$. Let $I$ be an interval on the real line $T$, and $D(I)$ be the event $\{x_t\in\Gamma at some t\in I\}$. Such a system of events $D(I)$ satisfies conditions 1.A–1.B.
Under some assumptions, in the Markov case, all such systems are described. The main result is applied to the analysis of a special $\sigma$-field in the space $T\times\Omega$.

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English version:
Theory of Probability and its Applications, 1976, 21:1, 144–148

Bibliographic databases:

Received: 24.06.1974

Citation: M. I. Taksar, “On events connected with reaching a set by sample paths of a stochastic process”, Teor. Veroyatnost. i Primenen., 21:1 (1976), 143–146; Theory Probab. Appl., 21:1 (1976), 144–148

Citation in format AMSBIB
\Bibitem{Tak76}
\by M.~I.~Taksar
\paper On events connected with reaching a~set by sample paths of a~stochastic process
\jour Teor. Veroyatnost. i Primenen.
\yr 1976
\vol 21
\issue 1
\pages 143--146
\mathnet{http://mi.mathnet.ru/tvp3301}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=402889}
\zmath{https://zbmath.org/?q=an:0366.60044}
\transl
\jour Theory Probab. Appl.
\yr 1976
\vol 21
\issue 1
\pages 144--148
\crossref{https://doi.org/10.1137/1121012}


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