Geodesic
On a limit behavior of a one-dimensional random walk with non-integrable impurity
Teoriâ slučajnyh processov, Tome 20 (2015) no. 2, pp. 97-104

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We consider the limit behavior of a one-dimensional symmetric random walk that is perturbed at zero. For the natural scaling of time and space the invariance principle is proved. The limit process is a skew Brownian motion.
Keywords: Skew Brownian motion, invariance principle, perturbed random walk. 
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     title = {On a limit behavior of a one-dimensional random walk with non-integrable impurity},
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Andrey Pilipenko; Lyudmila Sakhanenko. On a limit behavior of a one-dimensional random walk with non-integrable impurity. Teoriâ slučajnyh processov, Tome 20 (2015) no. 2, pp. 97-104. http://geodesic.mathdoc.fr/item/THSP_2015_20_2_a6/