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Large time behavior of interface solutions to the heat equation with Fisher-Wright white noise
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  • Published: September 1995

Large time behavior of interface solutions to the heat equation with Fisher-Wright white noise

  • Roger Tribe1 

Probability Theory and Related Fields volume 102, pages 289–311 (1995)Cite this article

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Summary

The one-dimensional heat equation driven by Fisher-Wright white noise is studied. From initial conditions with compact support, solutions retain this compact support and die out in finite time. There exist interface solutions which change from the value 1 to the value 0 in a finite region. The motion of the interface location is shown to approach that of a Brownian motion under rescaling. Solutions with a finite number of interfaces are approximated by a system of annihilating Brownian motions.

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Authors and Affiliations

  1. Weierstrass Institut für Angewandte Analysis und Stochastik, Mohrenstrasse 39, D-10117, Berlin, Germany

    Roger Tribe

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  1. Roger Tribe
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Tribe, R. Large time behavior of interface solutions to the heat equation with Fisher-Wright white noise. Probab. Th. Rel. Fields 102, 289–311 (1995). https://doi.org/10.1007/BF01192463

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  • Received: 08 November 1993

  • Revised: 16 August 1994

  • Issue Date: September 1995

  • DOI: https://doi.org/10.1007/BF01192463

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  • 60H15
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