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Long-time behaviour of nonautonomous SPDE's

Author

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  • Maslowski, Bohdan
  • Simão, Isabel

Abstract

It is proved that under suitable conditions the probability laws of two arbitrary solutions of the infinite dimensional stochastic equationdXt=AXt dt+f(t,Xt) dt+Q1/2 dWtconverge to each other, as time goes to infinity, in the strong (variational) topology. To this end, some lower estimates on the transition density of the solution, with respect to a certain Gaussian measure, are obtained. In addition, an explicit formula for the density is given, in the case where Q-1/2f is bounded.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:95:y:2001:i:2:p:285-309
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Goldys, B. & Maslowski, B., 2008. "The Ornstein-Uhlenbeck bridge and applications to Markov semigroups," Stochastic Processes and their Applications, Elsevier, vol. 118(10), pages 1738-1767, October.

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