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

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.

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Year of publication:	2009
Authors:	Funaki, Tadahisa ; Xie, Bin
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 119.2009, 2, p. 307-326
Publisher:	Elsevier
Keywords:	Stochastic heat equation Stochastic partial differential equation Lévy process

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008874319