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Asymptotic behaviour of a Brownian motion on exterior domains
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  • Published: March 2000

Asymptotic behaviour of a Brownian motion on exterior domains

  • Pierre Collet1,
  • Servet Martínez2 &
  • Jaime San Martín2 

Probability Theory and Related Fields volume 116, pages 303–316 (2000)Cite this article

Abstract.

We study the asymptotic behaviour of the transition density of a Brownian motion in ?, killed at ∂?, where ?c is a compact non polar set. Our main result concern dimension d = 2, where we show that the transition density p ? t (x, y) behaves, for large t, as u(x)u(y)(t(log t)2)−1 for x, y∈?, where u is the unique positive harmonic function vanishing on (∂?)r, such that u(x) ∼ log ∣x∣.

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Authors and Affiliations

  1. C.N.R.S., Physique Théorique, Ecole Polytechnique, 91128 Palaiseau Cedex, France. e-mail: collet@pth.polytechnique.fr, , , , , , FR

    Pierre Collet

  2. Universidad de Chile, Facultad de Ciencias Físicas y Matemáticas, Departamento de Ingeniería Matemática, Casilla 170-3 Correo 3, Santiago, Chile. e-mails: smartine@dim.uchile.cl; jsanmart@dim.uchile.cl, , , , , , CL

    Servet Martínez & Jaime San Martín

Authors
  1. Pierre Collet
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  2. Servet Martínez
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  3. Jaime San Martín
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Received: 29 January 1999 / Revised version: 11 May 1999

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Cite this article

Collet, P., Martínez, S. & San Martín, J. Asymptotic behaviour of a Brownian motion on exterior domains. Probab Theory Relat Fields 116, 303–316 (2000). https://doi.org/10.1007/s004400050251

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  • Issue Date: March 2000

  • DOI: https://doi.org/10.1007/s004400050251

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Keywords

  • Brownian Motion
  • Asymptotic Behaviour
  • Harmonic Function
  • Transition Density
  • Exterior Domain
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