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

Tadahisa Funaki and Bin Xie

Stochastic Processes and their Applications, 2009, vol. 119, issue 2, 307-326

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.

Keywords: Stochastic; heat; equation; Stochastic; partial; differential; equation; Lévy; process (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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