Exit times from equilateral triangles

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6 Citations (Scopus)

Abstract

In this paper we obtain a closed form expression of the expected exit time of a Brownian motion from equilateral triangles. We consider first the analogous problem for a symmetric random walk on the triangular lattice and show that it is equivalent to the ruin problem of an appropriate three player game. A suitable scaling of this random walk allows us to exhibit explicitly the relation between the respective exit times. This gives us the solution of the related Poisson equation. © 2003 Springer-Verlag New York Inc.
Original languageEnglish
Pages (from-to)43-53
JournalApplied Mathematics and Optimization
Volume49
DOIs
Publication statusPublished - 1 Dec 2003

Keywords

  • Brownian motion
  • Exit time
  • Poisson equation
  • Random walk

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