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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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/

[1] N. H. Bingham, C. M. Goldie, J. L. Teugels, Regular variation, Cambridge University Press, Cambridge, 1989 | MR | Zbl

[2] W. Feller, An Introduction to Probability Theory and Its Applications, v. 1, J. Wiley sons, 1960

[3] J. M. Harrison, L. A. Shepp, “On skew Brownian motion”, Ann. Probab., 9 (1981), 309–313 | DOI | MR | Zbl

[4] A. M. Iksanov, A. Yu. Pilipenko, A functional limit theorem for locally perturbed random walks, arXiv: 1504.06930

[5] A. Lejay, “On the constructions of the skew Brownian motion”, Probability Surveys, 3 (2006), 413–466 | DOI | MR | Zbl

[6] R. A. Minlos, E. A. Zhizhina, “Limit diffusion process for a non-homogeneous random walk on a one-dimensional lattice”, Russ. Math. Surv., 52 (1997), 327–340 | DOI | MR | Zbl

[7] A. Pilipenko, Yu. Prykhodko, “On a limit behavior of a sequence of Markov processes perturbed in a neighborhood of a singular point”, Ukrainian Math. Journal, 67:4 (2015), 499–516 | DOI | MR

[8] A. Yu. Pilipenko, Yu. E. Prykhodko, “Limit behavior of a simple random walk with non-integrable jump from a barrier”, Theor. Stoch. Proc., 19(35):1 (2014), 52–61 | MR | Zbl

[9] A. Yu. Pilipenko, Yu. E. Pryhod'ko, “Limit behavior of symmetric random walks with a membrane”, Theory Probab. Math. Stat., 85 (2012), 93–105 | DOI | MR | Zbl

[10] D. Szász, A. Telcs, “Random walk in an inhomogeneous medium with local impurities”, J. Stat. Physics, 26 (1981), 527–537 | DOI | MR | Zbl