Exit Times from Equilateral Triangles

Journal Article · Mon Dec 15 00:00:00 EST 2003 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-003-0779-1· OSTI ID:21067463

Alabert, Aureli; Farre, Merce ^[1]; Roy, Rahul ^[2]

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1. Departament de Matematiques, Universitat Autonoma de Barcelona, 08193 Bellaterra, Catalonia (Spain)
2. Centre de Recerca Matematica, Apartat 50, 08193 Bellaterra, Catalonia, SpainandIndian Statistical Institute, 7 S.J.S. Sansanwal Marg, New Delhi - 110016 (India)

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.

• OSTI ID: 21067463
• Journal Information: Applied Mathematics and Optimization, Vol. 49, Issue 1; Other Information: DOI: 10.1007/s00245-003-0779-1; Copyright (c) 2003 Springer-Verlag; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BROWNIAN MOVEMENT
GAME THEORY
GRAPH THEORY
MATHEMATICAL SOLUTIONS
POISSON EQUATION
RANDOMNESS