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Exit Times from Equilateral Triangles

Exit Times from Equilateral Triangles 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 latticeand 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 betweenthe respective exit times. This gives us the solution of the related Poisson equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics & Optimization Springer Journals

Exit Times from Equilateral Triangles

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References (9)

Publisher
Springer Journals
Copyright
Copyright © Springer-Verlag 2003
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-003-0779-1
Publisher site
See Article on Publisher Site

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 latticeand 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 betweenthe respective exit times. This gives us the solution of the related Poisson equation.

Journal

Applied Mathematics & Optimization – Springer Journals

Published: Dec 1, 2004

Keywords: Exit time; Random walk; Brownian motion; Poisson equation

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