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Stabilization by noise for a class of stochastic reaction-diffusion equations
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  • Published: 10 February 2005

Stabilization by noise for a class of stochastic reaction-diffusion equations

  • Sandra Cerrai1 

Probability Theory and Related Fields volume 133, pages 190–214 (2005)Cite this article

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  • 14 Citations

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Abstract.

We prove uniqueness, ergodicity and strongly mixing property of the invariant measure for a class of stochastic reaction-diffusion equations with multiplicative noise, in which the diffusion term in front of the noise may vanish and the deterministic part of the equation is not necessary asymptotically stable. To this purpose, we show that the L1-norm of the difference of two solutions starting from any two different initial data converges ℙ-a.s. to zero, as time goes to infinity.

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Authors and Affiliations

  1. Dip. Matematica per le Decisioni, Università di Firenze, Via C. Lombroso 6/17, 50134, Firenze, Italy

    Sandra Cerrai

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  1. Sandra Cerrai
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Additional information

This paper was written while the author was visiting the Scuola Normale Superiore, Pisa

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Cite this article

Cerrai, S. Stabilization by noise for a class of stochastic reaction-diffusion equations. Probab. Theory Relat. Fields 133, 190–214 (2005). https://doi.org/10.1007/s00440-004-0421-4

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  • Received: 22 March 2004

  • Revised: 04 December 2004

  • Published: 10 February 2005

  • Issue Date: October 2005

  • DOI: https://doi.org/10.1007/s00440-004-0421-4

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Keywords

  • Initial Data
  • Stochastic Process
  • Probability Theory
  • Invariant Measure
  • Mathematical Biology
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