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Almost sure asymptotics for the continuous parabolic Anderson model
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  • Published: December 2000

Almost sure asymptotics for the continuous parabolic Anderson model

  • J. Gärtner1,
  • W. König1 &
  • S.A. Molchanov2 

Probability Theory and Related Fields volume 118, pages 547–573 (2000)Cite this article

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  • 43 Citations

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Abstract.

We consider the parabolic Anderson problem ∂ t u = κΔu + ξ(x)u on ℝ+×ℝd with initial condition u(0,x) = 1. Here κ > 0 is a diffusion constant and ξ is a random homogeneous potential. We concentrate on the two important cases of a Gaussian potential and a shot noise Poisson potential. Under some mild regularity assumptions, we derive the second-order term of the almost sure asymptotics of u(t, 0) as t→∞.

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Authors and Affiliations

  1. Technische Universität, FB Mathematik, Str.des 17.Juni 136, 10623 Berlin, Germany. e-mail: jg@math.tu-berlin.de, , , , , , DE

    J. Gärtner & W. König

  2. Department of Mathematics, University of North Carolina, Charlotte, NC 28223-9998, USA, , , , , , US

    S.A. Molchanov

Authors
  1. J. Gärtner
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  2. W. König
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  3. S.A. Molchanov
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Additional information

Received: 26 July 1999 / Revised version: 6 April 2000 / Published online: 22 November 2000

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Cite this article

Gärtner, J., König, W. & Molchanov, S. Almost sure asymptotics for the continuous parabolic Anderson model. Probab Theory Relat Fields 118, 547–573 (2000). https://doi.org/10.1007/PL00008754

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  • Issue Date: December 2000

  • DOI: https://doi.org/10.1007/PL00008754

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Keywords

  • Diffusion Constant
  • Shot Noise
  • Important Case
  • Anderson Model
  • Regularity Assumption
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