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

 Teor. Veroyatnost. i Primenen., 1973, Volume 18, Issue 1, Pages 44–55 (Mi tvp2679)

Diffusion approximation of non-Markov random walks on differentiable manifolds

G. M. Sobko

Moscow

Abstract: The present paper considers limit theorems for sequences of non-Markov random walks on a differentiable manifold of $C^3$-class. The result obtained is a generalization of the classic theorem for sums of dependent random variables (theorem 1). This theorem is applied then to investigation of some special random walks on a Lie group $\mathfrak G$ admitting the “polar” factorization $\mathfrak G=\mathfrak R\cdot\mathfrak U$ where $\mathfrak U$ is a compact subgroup of $\mathfrak G$. Similarly to the well-known method of N. N. Bogolyubov for differential equations with a small parameter, it may be called the principle of (compact) averaging for triangle systems of random elements on Lie groups.

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English version:
Theory of Probability and its Applications, 1973, 18:1, 41–53

Bibliographic databases:

Citation: G. M. Sobko, “Diffusion approximation of non-Markov random walks on differentiable manifolds”, Teor. Veroyatnost. i Primenen., 18:1 (1973), 44–55; Theory Probab. Appl., 18:1 (1973), 41–53

Citation in format AMSBIB
\Bibitem{Sob73} \by G.~M.~Sobko \paper Diffusion approximation of non-Markov random walks on differentiable manifolds \jour Teor. Veroyatnost. i Primenen. \yr 1973 \vol 18 \issue 1 \pages 44--55 \mathnet{http://mi.mathnet.ru/tvp2679} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=317386} \zmath{https://zbmath.org/?q=an:0298.60049} \transl \jour Theory Probab. Appl. \yr 1973 \vol 18 \issue 1 \pages 41--53 \crossref{https://doi.org/10.1137/1118003}