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Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 3, Pages 549–557 (Mi tvp2667)  

Short Communications

The first problem of diffusion on differentiable manifolds

G. M. Sobko

Moscow

Abstract: Let $\{\xi_\Delta(k), k=0,1,…,n=n(\Delta)\}$be a sequence of random walks on a differentiable manifold $M$. In this paper, we obtain the classical conditions for convergence of $\xi_\Delta$ to an inhomogeneous diffusion process $\xi(t)$ in terms of weak convergence of transition probabilities $P_\Delta(t_k,x;t,\Gamma)$ using some modification of Khintchine's idea from [1]. One of many consequences of the result is a limit theorem for convolutions of noncommuting probability measures on Lie groups.

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English version:
Theory of Probability and its Applications, 1973, 17:3, 521–528

Bibliographic databases:

Received: 01.06.1971

Citation: G. M. Sobko, “The first problem of diffusion on differentiable manifolds”, Teor. Veroyatnost. i Primenen., 17:3 (1972), 549–557; Theory Probab. Appl., 17:3 (1973), 521–528

Citation in format AMSBIB
\Bibitem{Sob72}
\by G.~M.~Sobko
\paper The first problem of diffusion on differentiable manifolds
\jour Teor. Veroyatnost. i Primenen.
\yr 1972
\vol 17
\issue 3
\pages 549--557
\mathnet{http://mi.mathnet.ru/tvp2667}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=307355}
\zmath{https://zbmath.org/?q=an:0298.60048}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 17
\issue 3
\pages 521--528
\crossref{https://doi.org/10.1137/1117062}


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