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A Random Walk on Rectangles Algorithm

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Abstract

In this article, we introduce an algorithm that simulates efficiently the first exit time and position from a rectangle (or a parallelepiped) for a Brownian motion that starts at any point inside. This method provides an exact way to simulate the first exit time and position from any polygonal domain and then to solve some Dirichlet problems, whatever the dimension. This method can be used as a replacement or complement of the method of the random walk on spheres and can be easily adapted to deal with Neumann boundary conditions or Brownian motion with a constant drift.

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Authors and Affiliations

  1. Projet OMEGA, INRIA Lorraine and Institut Élie Cartan de Nancy (IECN), Campus scientifique, BP 239, 54506, Vandœuvre-lès-Nancy, CEDEX, France

    Madalina Deaconu & Antoine Lejay

Authors
  1. Madalina Deaconu
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  2. Antoine Lejay
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Correspondence to Madalina Deaconu.

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AMS 2000 Subject Classification

60C05, 65N

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Deaconu, M., Lejay, A. A Random Walk on Rectangles Algorithm. Methodol Comput Appl Probab 8, 135–151 (2006). https://doi.org/10.1007/s11009-006-7292-3

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  • DOI: https://doi.org/10.1007/s11009-006-7292-3

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