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Exit Times from Equilateral Triangles

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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.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia, Spain

    Aureli Alabert & Mercè Farré

  2. Centre de Recerca Matemàtica, Apartat 50, 08193 Bellaterra, Catalonia, Spain and Indian Statistical Institute, 7 S.J.S. Sansanwal Marg, New Delhi - 110016, India

    Rahul Roy

Authors
  1. Aureli Alabert
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  2. Mercè Farré
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  3. Rahul Roy
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Corresponding authors

Correspondence to Aureli Alabert, Mercè Farré or Rahul Roy.

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Alabert, A., Farré, M. & Roy, R. Exit Times from Equilateral Triangles. Appl Math Optim 49, 43–53 (2004). https://doi.org/10.1007/s00245-003-0779-1

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  • DOI: https://doi.org/10.1007/s00245-003-0779-1

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