The heat equation with time-independent multiplicative stable Lévy noise |
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Authors: | Carl Mueller Leonid Mytnik Aurel Stan |
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Affiliation: | 1. Department of Mathematics, University of Rochester, Rochester, NY 14627, USA;2. Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, Haifa 32000, Israel;3. Department of Mathematics, The Ohio State University at Marion, 1465 Mt Vernon Avenue, Marion, OH 43302, USA |
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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<1 and p?1. |
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Keywords: | Primary 60H15 secondary 35R60 35K05 |
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