Geodesic
Limit theorems for asymmetric random walk
Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 4, pp. 731-736

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The paper deals with an asymmetric random walk with transition probabilities $p_{k,k+1}=p$, $p_{k,k-1}=1-p=q$. Let $S_k$ be the location of the system at time $k$; $f(k)$ be a function determined for all integers $k$. For some class of functions $f$ the limit behavior as $p-q\to0$ of the functionals of the type $\sum_{k=0}^\infty f(S_k)$ is studied. 
@article{TVP_1970_15_4_a11,
     author = {O. G. Miklukhin},
     title = {Limit theorems for asymmetric random walk},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {731--736},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_4_a11/}
}
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O. G. Miklukhin. Limit theorems for asymmetric random walk. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 4, pp. 731-736. http://geodesic.mathdoc.fr/item/TVP_1970_15_4_a11/