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arXiv · 1509.03529

On a limit behavior of a sequence of Markov processes perturbed in a neighborhood of a singular point

Andrey Pilipenko·Yuriy Prykhodko
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Abstract

We study a limit behavior of a sequence of Markov processes (or Markov chains) such that their distributions outside of any neighborhood of a "singular" point attract to some probability law. In any neighborhood of this point the behavior may be irregular. As an example of the general result we consider a symmetric random walk with the unit jump that is perturbed in a neighborhood of 0. The invariance principle is obtained under standard scaling of time and space. The limit process turns out to be a skew Brownian motion.

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Andrey Pilipenko, Yuriy Prykhodko. 2015-09-11. On a limit behavior of a sequence of Markov processes perturbed in a neighborhood of a singular point. https://arxiv.org/abs/1509.03529

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