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 Teor. Veroyatnost. i Primenen., 1956, Volume 1, Issue 1, Pages 25–37 (Mi tvp4984)

Markov Processes and Semigroups of Operators

E. B. Dynkin

Moscow

Abstract: In this paper the relations between various semigroups of operators and between various infinitesimal operators connected with a homogeneous in t Markov process are investigated. General conditions are established under which the Markov process is determined by its corresponding infinitesimal operator.
Let $U_t$ be a semigroup of linear operators in the Banach space $L$ such that $\|U_t\|\leq1$. Let $T_t=U_t$ be an adjoint semigroup in the conjugate space $B=L^*$. More abstractly the main object of this paper can be characterized as the study of semigroups $T_t$ and its infinitesimal operators in strong and weak topologies of space $B$.

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English version:
Theory of Probability and its Applications, 1956, 1:1, 22–33

Citation: E. B. Dynkin, “Markov Processes and Semigroups of Operators”, Teor. Veroyatnost. i Primenen., 1:1 (1956), 25–37; Theory Probab. Appl., 1:1 (1956), 22–33

Citation in format AMSBIB
\Bibitem{Dyn56} \by E.~B.~Dynkin \paper Markov Processes and Semigroups of Operators \jour Teor. Veroyatnost. i Primenen. \yr 1956 \vol 1 \issue 1 \pages 25--37 \mathnet{http://mi.mathnet.ru/tvp4984} \transl \jour Theory Probab. Appl. \yr 1956 \vol 1 \issue 1 \pages 22--33 \crossref{https://doi.org/10.1137/1101003}