A Random Walk on Rectangles Algorithm

Madalina Deaconu () and Antoine Lejay ()
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Madalina Deaconu: INRIA Lorraine and Institut Élie Cartan de Nancy (IECN)
Antoine Lejay: INRIA Lorraine and Institut Élie Cartan de Nancy (IECN)

Methodology and Computing in Applied Probability, 2006, vol. 8, issue 1, 135-151

Abstract: 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.

Keywords: Monte Carlo method; Laplace operator; Random walk on spheres/squares; Green functions; Dirichlet/Neumann problem (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s11009-006-7292-3

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