Brownian motion in a wedge with variable skew reflection

Rogers, L. C. G.

doi:10.1090/S0002-9947-1991-1008701-0

Brownian motion in a wedge with variable skew reflection
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by L. C. G. Rogers

Trans. Amer. Math. Soc. 326 (1991), 227-236

DOI: https://doi.org/10.1090/S0002-9947-1991-1008701-0

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Abstract:

Does planar Brownian motion confined to a wedge by skew reflection on the sides approach the vertex of the wedge? This question has been answered by Varadhan and Williams in the case where the direction of reflection is constant on each of the sides, but here we address the question when the direction reflected is allowed to vary. A necessary condition, and a sufficient condition, are obtained for the vertex to be reached. The conditions are of a geometric nature, and the gap between them is quite small.

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