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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 4, Pages 640–657 (Mi tvp4318)

Nonhomogeneous semigroups of measures on compact Lie groups

V. M. Maksimov

Moscow

Abstract: A system of probability measures $\{P_{uv}\}$, $a\leq u\leq v\leq b$, on a group $G$ is called a non-homogeneous semi-group if
(i) $P_{uv}P_{uw}=P_{uw}$;
(ii) $P_{t,t+\Delta}\to\delta (e)$ weakly ($\delta (e)$ is the degenerate distribution concentrated at the identity element of $G$);
(iii) $P_{tt}=\delta (e)$, $a\leq t\leq b$. Semi-groups generate stochastically continuous processes with independent increments on $G$ and vice versa.
In the paper, it is proved that for the existence (at each point $t$, $a\leq t\leq b$) of the generator of $P_{t,t+\Delta}$ ($\Delta\to 0$) on $C_2$ it is necessary and sufficient that the Fourier coefficients of measures $P_{uv}$ be continuously differentiable in $u$ and $v$. The generator is then a Hant operator.

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English version:
Theory of Probability and its Applications, 1973, 17:4, 601–619

Bibliographic databases:

Citation: V. M. Maksimov, “Nonhomogeneous semigroups of measures on compact Lie groups”, Teor. Veroyatnost. i Primenen., 17:4 (1972), 640–657; Theory Probab. Appl., 17:4 (1973), 601–619

Citation in format AMSBIB
\Bibitem{Mak72} \by V.~M.~Maksimov \paper Nonhomogeneous semigroups of measures on compact Lie groups \jour Teor. Veroyatnost. i Primenen. \yr 1972 \vol 17 \issue 4 \pages 640--657 \mathnet{http://mi.mathnet.ru/tvp4318} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=317365} \zmath{https://zbmath.org/?q=an:0315.60007} \transl \jour Theory Probab. Appl. \yr 1973 \vol 17 \issue 4 \pages 601--619 \crossref{https://doi.org/10.1137/1117074}