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The heat equation with time-independent multiplicative stable Lévy noise

Author

Listed:
  • Mueller, Carl
  • Mytnik, Leonid
  • Stan, Aurel

Abstract

We study the heat equation with a random potential term. The potential is a one-sided stable noise, with positive jumps, which does not depend on time. To avoid singularities, we define the equation in terms of a construction similar to the Skorokhod integral or Wick product. We give a criterion for existence based on the dimension of the space variable, and the parameter p of the stable noise. Our arguments are different for p

Suggested Citation

  • Mueller, Carl & Mytnik, Leonid & Stan, Aurel, 2006. "The heat equation with time-independent multiplicative stable Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 70-100, January.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:1:p:70-100
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    References listed on IDEAS

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    1. Mueller, Carl, 1998. "The heat equation with Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 67-82, May.
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