Geodesic
Central Limit Theorem for a Class of Nonhomogeneous Random Walks
Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 751-757 
D. A. Yarotskii. Central Limit Theorem for a Class of Nonhomogeneous Random Walks. Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 751-757. http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a10/
@article{MZM_2001_69_5_a10,
     author = {D. A. Yarotskii},
     title = {Central {Limit} {Theorem} for a {Class} of {Nonhomogeneous} {Random} {Walks}},
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     pages = {751--757},
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     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\eta_t$.

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