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Teoriya Veroyatnostei i ee Primeneniya, 1980, Volume 25, Issue 2, Pages 389–393
(Mi tvp1184)
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This article is cited in 13 scientific papers (total in 13 papers)
Short Communications
Any Markov process in a Borel space has a transition function
S. E. Kuznecov Moscow
Abstract:
The most natural way to define «Markov process» $x_t$ is to say that it is a stochastic process with the Markov property. However, in some of the most interesting applications it is possible to consider only the processes with transition function, which is a family $\{p_t^s(x,\Gamma)\}$ of conditional distributions of $x_t$ given $x_s$, satisfying Kolmogorov–Chapman equation $p_t^s p_u^t=p_u^s$, $s<t<u$. We prove that the Markov process has the transition function if its state space is universal (i. e. it is isomorphic to a universally measurable subset of a Polish space).
Received: 18.12.1979
Citation:
S. E. Kuznecov, “Any Markov process in a Borel space has a transition function”, Teor. Veroyatnost. i Primenen., 25:2 (1980), 389–393; Theory Probab. Appl., 25:2 (1981), 384–388
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https://www.mathnet.ru/eng/tvp1184 https://www.mathnet.ru/eng/tvp/v25/i2/p389
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Abstract page: | 409 | Full-text PDF : | 147 | First page: | 1 |
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