학술논문
Exit Times from Equilateral Triangles.
Document Type
Article
Author
Source
Subject
*WIENER processes
*TRIANGLES
*POISSON'S equation
*LATTICE theory
*SCALING laws (Statistical physics)
*RANDOM walks
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Language
ISSN
0095-4616
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. [ABSTRACT FROM AUTHOR]