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Reflected Brownian motion in generic triangles and wedges

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  • Kager, Wouter

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.

Suggested Citation

  • Kager, Wouter, 2007. "Reflected Brownian motion in generic triangles and wedges," Stochastic Processes and their Applications, Elsevier, vol. 117(5), pages 539-549, May.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:5:p:539-549
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    Cited by:

    1. S. Franceschi, 2021. "Green’s Functions with Oblique Neumann Boundary Conditions in the Quadrant," Journal of Theoretical Probability, Springer, vol. 34(4), pages 1775-1810, December.
    2. Bras, Pierre & Kohatsu-Higa, Arturo, 2023. "Simulation of reflected Brownian motion on two dimensional wedges," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 349-378.

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