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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2001, Volume 69, Issue 5, Pages 751–757 (Mi mz538)

Central Limit Theorem for a Class of Nonhomogeneous Random Walks

D. A. Yarotskii

M. V. Lomonosov Moscow State University

Abstract: A spatially nonhomogeneous random walk $\eta_t$ on the grid $\mathbb Z^\nu=\mathbb Z^m\times\mathbb Z^n$ is considered. Let $\eta_t^0$ be a random walk homogeneous in time and space, and let $\eta_t$ be obtained from it by changing transition probabilities on the set $A=\overline A\times\mathbb Z^n$, $|\overline A|<\infty$, so that the walk remains homogeneous only with respect to the subgroup $\mathbb Z^n$ of the group $\mathbb Z^\nu$. It is shown that if $m\ge2$ or the drift is distinct from zero, then the central limit theorem holds for $\eta_t$.

DOI: https://doi.org/10.4213/mzm538

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English version:
Mathematical Notes, 2001, 69:5, 690–695

Bibliographic databases:

UDC: 519
Revised: 05.04.2000

Citation: D. A. Yarotskii, “Central Limit Theorem for a Class of Nonhomogeneous Random Walks”, Mat. Zametki, 69:5 (2001), 751–757; Math. Notes, 69:5 (2001), 690–695

Citation in format AMSBIB
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