On a limit behavior of a one-dimensional random walk with non-integrable impurity

Andrey Pilipenko, Lyudmila Sakhanenko
Theory of Stochastic Processes
Vol.20 (36), no.2, 2015, pp.97-104
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.