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Simulation of reflected Brownian motion on two dimensional wedges

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  • Bras, Pierre
  • Kohatsu-Higa, Arturo

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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:156:y:2023:i:c:p:349-378
    DOI: 10.1016/j.spa.2022.11.011
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    References listed on IDEAS

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    1. Metzler, Adam, 2010. "On the first passage problem for correlated Brownian motion," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 277-284, March.
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    3. Vadim Kaushansky & Alexander Lipton & Christoph Reisinger, 2017. "Transition probability of Brownian motion in the octant and its application to default modeling," Papers 1801.00362, arXiv.org, revised May 2018.
    4. Kager, Wouter, 2007. "Reflected Brownian motion in generic triangles and wedges," Stochastic Processes and their Applications, Elsevier, vol. 117(5), pages 539-549, May.
    5. Madalina Deaconu & Antoine Lejay, 2006. "A Random Walk on Rectangles Algorithm," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 135-151, March.
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