Reflected Brownian motion in generic triangles and wedges |
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Authors: | Wouter Kager |
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Institution: | Instituut voor Theoretische Fysica, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands |
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Abstract: | Consider a generic triangle in the upper half of the complex plane with one side on the real line. This paper presents a tailored construction of a discrete random walk whose continuum limit is a Brownian motion in the triangle, reflected instantaneously on the left and right sides with constant reflection angles. Starting from the top of the triangle, it is evident from the construction that the reflected Brownian motion lands with the uniform distribution on the base. This raises some questions on the possible distributions of hulls generated by local processes. |
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Keywords: | 60J65 60J99 |
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