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

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  • Funaki, Tadahisa
  • Xie, Bin

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.

Suggested Citation

  • Funaki, Tadahisa & Xie, Bin, 2009. "A stochastic heat equation with the distributions of Lévy processes as its invariant measures," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 307-326, February.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:2:p:307-326
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    References listed on IDEAS

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    1. Albeverio, Sergio & Wu, Jiang-Lun & Zhang, Tu-Sheng, 1998. "Parabolic SPDEs driven by Poisson white noise," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 21-36, May.
    2. Mueller, Carl, 1998. "The heat equation with Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 67-82, May.
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    Cited by:

    1. Wang, Ran & Xu, Lihu, 2018. "Asymptotics for stochastic reaction–diffusion equation driven by subordinate Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1772-1796.

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