The heat equation with time-independent multiplicative stable Lévy noise

Carl Mueller, Leonid Mytnik and Aurel Stan

Stochastic Processes and their Applications, 2006, vol. 116, issue 1, 70-100

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

Keywords: Heat; equation; Noise; Stochastic; partial; differential; equations (search for similar items in EconPapers)
Date: 2006
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