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Invariant measures for stochastic heat equations with unbounded coefficients

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  • Assing, Sigurd
  • Manthey, Ralf

Abstract

The paper deals with the Cauchy problem in of a stochastic heat equation . The locally lipschitz drift coefficient f can have polynomial growth while the diffusion coefficient [sigma] is supposed to be lipschitz but not necessarily bounded. Of course, for the existence of a solution alone, a certain dissipativity of f is needed. Applying the comparison method, a condition on the strength of this dissipativity is derived even ensuring the existence of an invariant measure.

Suggested Citation

  • Assing, Sigurd & Manthey, Ralf, 2003. "Invariant measures for stochastic heat equations with unbounded coefficients," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 237-256, February.
    • Handle: RePEc:eee:spapps:v:103:y:2003:i:2:p:237-256
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    References listed on IDEAS

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    1. Brzezniak, Zdzislaw & Gatarek, Dariusz, 1999. "Martingale solutions and invariant measures for stochastic evolution equations in Banach spaces," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 187-225, December.
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    Cited by:

    1. Oleksandr Misiats & Oleksandr Stanzhytskyi & Nung Kwan Yip, 2016. "Existence and Uniqueness of Invariant Measures for Stochastic Reaction–Diffusion Equations in Unbounded Domains," Journal of Theoretical Probability, Springer, vol. 29(3), pages 996-1026, September.
    2. Yue Li & Shijie Shang & Jianliang Zhai, 2024. "Large Deviation Principle for Stochastic Reaction–Diffusion Equations with Superlinear Drift on $$\mathbb {R}$$ R Driven by Space–Time White Noise," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3496-3539, November.

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