A Random Walk on Rectangles Algorithm

  • Madalina Deaconu
  • Antoine Lejay


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.


Monte Carlo method Laplace operator Random walk on spheres/squares Green functions Dirichlet/Neumann problem 


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© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Projet OMEGAINRIA Lorraine and Institut Élie Cartan de Nancy (IECN)Vandœuvre-lès-NancyFrance

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