Probability Theory and Related Fields

, Volume 108, Issue 3, pp 417–439

Exponential decay rate of survival probability in a disastrous random environment

  • Tokuzo Shiga


We study the exponential decay rate of the survival probability up to time t>0 of a random walker moving in Zopf;d in a temporally and spatially fluctuating random environment. When the random walker has a speed parameter κ>0, we investigate the influence of κ on the exponential decay rate λ(d,κ). In particular we prove that for any fixed d≥1, λ(d,κ) behaves like as logκ as κ↘0.

Mathematics Subject Classification (1991): Primary 60K35 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Tokuzo Shiga
    • 1
  1. 1.Department of Applied Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152, Japan (e-mail:

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