A stochastic heat equation with the distributions of Lévy processes as its invariant measures

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Abstract

We consider a linear heat equation on a half line with an additive noise chosen properly in such a manner that its invariant measures are a class of distributions of Lévy processes. Our assumption on the corresponding Lévy measure is, in general, mild except that we need its integrability to show that the distributions of Lévy processes are the only invariant measures of the stochastic heat equation.

Original languageEnglish
Pages (from-to)307-326
Number of pages20
JournalStochastic Processes and their Applications
Volume119
Issue number2
DOIs
Publication statusPublished - 2009 Feb 1

Keywords

  • Lévy process
  • Stochastic heat equation
  • Stochastic partial differential equation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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