This article is cited in 2 papers

Short Communications

On the starting points of wanderings of Markov processes

E. B. Dynkin, A. A. Yushkevich

Moscow

Abstract: Let $x_t$ be a Markov process on $E$ and $D$ be a subset of $E$. We will call a wandering any connected component of the set $\{t\colon x_t\in D\}$. Denote by $\overline x_t$ the process obtained from $x_t$ by killing at the first exit time out of $D$. It is proved that, under some conditions, with probability 1, every wandering starts at a point of the Martin boundary corresponding to $\overline x_t$ (i.e. the limit in (3) exists).

Received: 25.12.1967

 English version: Theory of Probability and its Applications, 1968, 13:3, 468–470

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