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The compact support property for solutions to the heat equation with noise
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  • Published: September 1992

The compact support property for solutions to the heat equation with noise

  • Carl Mueller1 &
  • Edwin A. Perkins2 

Probability Theory and Related Fields volume 93, pages 325–358 (1992)Cite this article

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  • 34 Citations

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Summary

We consider all solutions of a martingale problem associated with the stochastic pde\(u_t = \tfrac{1}{2}u_{xx} + u^\gamma \dot W\) and show thatu(t,·) has compact support for allt≧0 ifu(0,·) does and if γ<1. This extends a result of T. Shiga who derived this compact support property for γ≦1/2 and complements a result of C. Mueller who proved this property fails if γ≧1.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Rochester, 14620, Rochester, NY, USA

    Carl Mueller

  2. Department of Mathematics, University of British Columbia, V6T 1Z2, Vancouver, B.C., Canada

    Edwin A. Perkins

Authors
  1. Carl Mueller
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  2. Edwin A. Perkins
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Additional information

The author's research was supported by an NSF grant and an NSERC operating grant

The author's research was supported by an NSERC operating grant

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Mueller, C., Perkins, E.A. The compact support property for solutions to the heat equation with noise. Probab. Th. Rel. Fields 93, 325–358 (1992). https://doi.org/10.1007/BF01193055

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  • Received: 25 July 1991

  • Revised: 14 February 1992

  • Issue Date: September 1992

  • DOI: https://doi.org/10.1007/BF01193055

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Compact Support
  • Heat Equation
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