Probability Theory and Related Fields

, Volume 132, Issue 3, pp 321–355

Lyapunov exponent for the parabolic anderson model with lévy noise

Article

DOI: 10.1007/s00440-004-0346-y

Cite this article as:
Cranston, M., Mountford, T. & Shiga, T. Probab. Theory Relat. Fields (2005) 132: 321. doi:10.1007/s00440-004-0346-y
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Abstract.

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

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where {Yx:xZd} is a field of independent Lévy processes and Δ is the discrete Laplacian.

Mathematics Subject Classification (2000):

Primary 60H15 60H30 Secondary 60G15 60K35 

Keywords

Parabolic Anderson model Feynman-Kac formula Lyapunov exponent Block argument 

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA
  2. 2.DMA, EPFLSwitzerland
  3. 3.MathematicsTokyo Inst. of Tech.TokyoJapan

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