### 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.