@article{Pilipenko_Prikhod’ko_2015, title={On the Limit Behavior of a Sequence of Markov Processes Perturbed in a Neighborhood of the Singular Point}, volume={67}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2000}, abstractNote={We study the limit behavior of a sequence of Markov processes whose distributions outside any neighborhood of a “singular” point are attracted to a certain probability law. In any neighborhood of this point, the limit behavior can be irregular. As an example of application of the general result, we consider a symmetric random walk with unit jumps perturbed in the neighborhood of the origin. The invariance principle is established for the standard time and space scaling. The limit process is a skew Brownian motion.}, number={4}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={PilipenkoA. Yu. and Prikhod’koYu. E.}, year={2015}, month={Apr.}, pages={499-516} }