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Lyapunov exponent for the parabolic anderson model with lévy noise
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  • Published: 03 May 2005

Lyapunov exponent for the parabolic anderson model with lévy noise

  • M. Cranston1,
  • T. S. Mountford2 &
  • T. Shiga3 

Probability Theory and Related Fields volume 132, pages 321–355 (2005)Cite this article

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Abstract.

We consider the asymptotic almost sure behavior of the solution of the equation

where {Y x :x ∈ Zd} is a field of independent Lévy processes and Δ is the discrete Laplacian.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Irvine, Irvine, CA, 92697-3875, USA

    M. Cranston

  2. DMA, EPFL, CH-1015, Switzerland

    T. S. Mountford

  3. Mathematics, Tokyo Inst. of Tech., Tokyo, 152-8551, Japan

    T. Shiga

Authors
  1. M. Cranston
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  2. T. S. Mountford
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  3. T. Shiga
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Corresponding author

Correspondence to M. Cranston.

Additional information

Research of the first two authors supported in part by a grant from NSF, of the third author by JSPS Grant-in-Aid for Scientific Research, Kiban(C) 13640103

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Cite this article

Cranston, M., Mountford, T. & Shiga, T. Lyapunov exponent for the parabolic anderson model with lévy noise. Probab. Theory Relat. Fields 132, 321–355 (2005). https://doi.org/10.1007/s00440-004-0346-y

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  • Received: 07 November 2002

  • Revised: 04 February 2004

  • Published: 03 May 2005

  • Issue Date: July 2005

  • DOI: https://doi.org/10.1007/s00440-004-0346-y

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Mathematics Subject Classification (2000):

  • Primary 60H15
  • 60H30
  • Secondary 60G15
  • 60K35

Keywords

  • Parabolic Anderson model
  • Feynman-Kac formula
  • Lyapunov exponent
  • Block argument
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