Reflected Brownian Motion with Drift in a Wedge

Peter Lakner; Ziran Liu; Josh Reed

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arXiv · 2204.10941

Reflected Brownian Motion with Drift in a Wedge

Peter Lakner·Ziran Liu·Josh Reed

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Abstract

We study reflecting Brownian motion with drift constrained to a wedge in the plane. Our first set of results provide necessary and sufficient conditions for existence and uniqueness of a solution to the corresponding submartingale problem with drift, and show that its solution possesses the Markov and Feller properties. Next, we study a version of the problem with absorption at the vertex of the wedge. In this case, we provide a condition for existence and uniqueness of a solution to the problem and some results on the probability of the vertex being reached.

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Peter Lakner, Ziran Liu, Josh Reed. 2022-04-22. Reflected Brownian Motion with Drift in a Wedge. https://arxiv.org/abs/2204.10941

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