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 Teor. Veroyatnost. i Primenen., 1961, Volume 6, Issue 2, Pages 228–231 (Mi tvp4771)

Short Communications

Invariability of the Strong Markov Property in the Transformations of Dynkin

Leung Chi-son

Moscow

Abstract: E. B. Dynkin in [2] has defined a large class of transformations of Markov processes. He calls processes obtained by these transformations $\widetilde X$ and $(\alpha,\xi)$-subprocesses of the process $X$. In this paper we prove that if the process $X$ is a strong Markov process, then, with some conditions imposed on $\alpha$ and $\xi$, the $(\alpha,\xi)$-subprocess will also be a strong Markov process. One special case of a $(\alpha,\xi)$ subprocess has been examined earlier by E. B. Dynkin in his book [1]. He proved in particular that the strong Markov property does not change in the formation of subprocesses. We show that the method he used for the special case can be carried over to the general case.

Full text: PDF file (429 kB)

English version:
Theory of Probability and its Applications, 1961, 6:2, 209–211

Citation: Leung Chi-son, “Invariability of the Strong Markov Property in the Transformations of Dynkin”, Teor. Veroyatnost. i Primenen., 6:2 (1961), 228–231; Theory Probab. Appl., 6:2 (1961), 209–211

Citation in format AMSBIB
\Bibitem{Leu61} \by Leung~Chi-son \paper Invariability of the Strong Markov Property in the Transformations of Dynkin \jour Teor. Veroyatnost. i Primenen. \yr 1961 \vol 6 \issue 2 \pages 228--231 \mathnet{http://mi.mathnet.ru/tvp4771} \transl \jour Theory Probab. Appl. \yr 1961 \vol 6 \issue 2 \pages 209--211 \crossref{https://doi.org/10.1137/1106027}