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Teor. Veroyatnost. i Primenen., 1977, Volume 22, Issue 4, Pages 791–812 (Mi tvp3627)  

Construction of a regular split process

S. E. Kuznecov

Moscow

Abstract: In this paper, we develop the approach to the general theory of Markov processes proposed in [4]. Let $x_t$ be an (inhomogeneous) Markov process. The right regularization $x_{t+}$ and the left regularization $x_{t-}$ of the process $x_t$ are constructed. They have the following properties. Let $t$ be a real number and $A$ be an event belonging to the «future» $\mathscr F_{>t}$. Then, almost surely, the function $\mathbf P_{t+,x_{t+}}(A)$ is the right-continuous modification of $\mathbf P_{t-,x_{t-}}(A)$ and $\mathbf P_{t-,x_{t-}}(A)$ is the left-continuous modification of $\mathbf P_{t+,x_{t+}}(A)$, where $\mathbf P_{s+,x}$ (resp. $\mathbf P_{s-,x}$) are the transition probabilities of $x_{t+}$ (resp. $x_{t-}$).

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English version:
Theory of Probability and its Applications, 1978, 22:4, 773–793

Bibliographic databases:

Received: 27.11.1975

Citation: S. E. Kuznecov, “Construction of a regular split process”, Teor. Veroyatnost. i Primenen., 22:4 (1977), 791–812; Theory Probab. Appl., 22:4 (1978), 773–793

Citation in format AMSBIB
\Bibitem{Kuz77}
\by S.~E.~Kuznecov
\paper Construction of a~regular split process
\jour Teor. Veroyatnost. i Primenen.
\yr 1977
\vol 22
\issue 4
\pages 791--812
\mathnet{http://mi.mathnet.ru/tvp3627}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=483032}
\zmath{https://zbmath.org/?q=an:0387.60082}
\transl
\jour Theory Probab. Appl.
\yr 1978
\vol 22
\issue 4
\pages 773--793
\crossref{https://doi.org/10.1137/1122089}


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