The heat equation with time-independent multiplicative stable Lévy noise

Carl Mueller; Leonid Mytnik; Aurel Stan

doi:10.1016/j.spa.2005.08.001

The heat equation with time-independent multiplicative stable Lévy noise

Carl Mueller, Leonid Mytnik, Aurel Stan

Data and Decision Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	70-100
Number of pages	31
Journal	Stochastic Processes and their Applications
Volume	116
Issue number	1
DOIs	https://doi.org/10.1016/j.spa.2005.08.001
State	Published - Jan 2006

Keywords

Heat equation
Noise
Stochastic partial differential equations

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/j.spa.2005.08.001

Cite this

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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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KW - Heat equation

KW - Noise

KW - Stochastic partial differential equations

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The heat equation with time-independent multiplicative stable Lévy noise

Abstract

Keywords

ASJC Scopus subject areas

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