Diffusion approximation of non-Markov random walks on differentiable manifolds
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 44-55
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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.
@article{TVP_1973_18_1_a2,
author = {G. M. Sobko},
title = {Diffusion approximation of {non-Markov} random walks on differentiable manifolds},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {44--55},
publisher = {mathdoc},
volume = {18},
number = {1},
year = {1973},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a2/}
}
G. M. Sobko. Diffusion approximation of non-Markov random walks on differentiable manifolds. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 44-55. http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a2/