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arXiv · 1511.01043

On a Brownian motion with a hard membrane

Vidyadhar Mandrekar·Andrey Pilipenko
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Abstract

Local perturbations of a Brownian motion are considered. As a limit we obtain a non-Markov process that behaves as a reflected Brownian motion on the positive half line until its local time at zero reaches some exponential level, then changes a sign and behaves as a reflected Brownian motion on the negative half line until some stopping time, etc.

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Vidyadhar Mandrekar, Andrey Pilipenko. 2017-03-22. On a Brownian motion with a hard membrane. https://doi.org/10.1016/j.spl.2016.02.005

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