Simulation of reflected Brownian motion on two dimensional wedges

Pierre Bras and Arturo Kohatsu-Higa

Stochastic Processes and their Applications, 2023, vol. 156, issue C, 349-378

Abstract: We study Brownian motion in two dimensions, which is reflected, stopped or killed in a wedge represented as the intersection of two half spaces. First, we provide explicit density formulas, hinted by the method of images. These explicit expressions rely on infinite oscillating sums of Bessel functions and may demand computationally costly procedures. We propose suitable recursive algorithms for the simulation of the laws of reflected and stopped Brownian motion which are based on generalizations of the reflection principle in two dimensions. We study and give bounds for the complexity of the proposed algorithms.

Keywords: Reflected Brownian motion; Wedge; Hitting times; Reflection principle; Method of images; Monte Carlo simulation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2022.11.011

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