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Qualitative behaviour of solutions of stochastic reaction-diffusion equations

Author

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  • Manthey, Ralf
  • Maslowski, Bohdan

Abstract

We consider semilinear stochastic evolution equations driven by a cylindrical Wiener process. They can be used as models for stochastic reaction-diffusion systems. Under certain conditions we prove existence, uniqueness and ergodicity of the invariant measure and the strong law of large numbers. For this purpose a Girsanov type theorem is also proved. These results are applied to stochastic-reaction diffusion equations appearing in physics.

Suggested Citation

  • Manthey, Ralf & Maslowski, Bohdan, 1992. "Qualitative behaviour of solutions of stochastic reaction-diffusion equations," Stochastic Processes and their Applications, Elsevier, vol. 43(2), pages 265-289, December.
    • Handle: RePEc:eee:spapps:v:43:y:1992:i:2:p:265-289
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    Cited by:

    1. Maslowski, Bohdan & Simão, Isabel, 2001. "Long-time behaviour of nonautonomous SPDE's," Stochastic Processes and their Applications, Elsevier, vol. 95(2), pages 285-309, October.
    2. 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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