Exit Times from Equilateral Triangles

Alabert, Aureli ; Farré, Mercè ; Roy, Rahul (2004) Exit Times from Equilateral Triangles Applied Mathematics & Optimization, 49 (1). pp. 43-53. ISSN 0095-4616

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Official URL: http://www.springerlink.com/content/a88p4q0r4k74be...

Related URL: http://dx.doi.org/10.1007/s00245-003-0779-1


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.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Random Walk; Brownian Motion; Poisson Equation
ID Code:50201
Deposited On:22 Jul 2011 14:04
Last Modified:23 Nov 2011 18:04

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