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.
https://hal.inria.fr/inria-00092424
Contributor : Antoine Lejay
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Submitted on : Sunday, September 10, 2006 - 12:36:11 PM
Last modification on : Saturday, January 27, 2018 - 1:31:50 AM
Long-term archiving on: Tuesday, April 6, 2010 - 12:52:07 AM
Madalina Deaconu, Antoine Lejay. A random walk on rectangles algorithm. Methodology and Computing in Applied Probability, Springer Verlag, 2006, 8 (1), pp.135-151. ⟨10.1007/s11009-006-7292-3⟩. ⟨inria-00092424⟩
