On a limit behavior of a random walk with modifications at zero

Andrey Pilipenko; Vladislav Khomenko

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arXiv · 1611.02048

On a limit behavior of a random walk with modifications at zero

Andrey Pilipenko·Vladislav Khomenko

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Abstract

We consider the limit behavior of a one-dimensional random walk with unit jumps whose transition probabilities are modified every time the walk hits zero. The invariance principle is proved in the scheme of series where the size of modifications depends on the number of series. For the natural scaling of time and space arguments the limit process is (i) a Brownian motion if modifications are "small", (ii) a linear motion with a random slope if modifications are "large", and (iii) the limit process satisfies an SDE with a local time of unknown process in a drift if modifications are "moderate".

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Andrey Pilipenko, Vladislav Khomenko. 2016-11-07. On a limit behavior of a random walk with modifications at zero. https://arxiv.org/abs/1611.02048

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