Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Exit Times from Equilateral Triangles

Journal Article · · Applied Mathematics and Optimization
;  [1];  [2]
  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, Journal Name: Applied Mathematics and Optimization Journal Issue: 1 Vol. 49; ISSN 0095-4616
Country of Publication:
United States
Language:
English

Similar Records

Post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem
Journal Article · Fri Apr 15 00:00:00 EDT 2011 · Physical Review. D, Particles Fields · OSTI ID:21541492

On continuous-time two person full-information best choice problem with imperfect observation
Conference · Fri Dec 30 23:00:00 EST 1994 · OSTI ID:36403

On the chromatic number of a space with forbidden equilateral triangle
Journal Article · Tue Sep 30 00:00:00 EDT 2014 · Sbornik. Mathematics · OSTI ID:22364894