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Pathwise global attractors for stationary random dynamical systems
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  • Published: March 1993

Pathwise global attractors for stationary random dynamical systems

  • Zdzislaw Brzeźniak1,
  • Marek Capiński1 &
  • Franco Flandoli2 

Probability Theory and Related Fields volume 95, pages 87–102 (1993)Cite this article

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  • 40 Citations

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Summary

The asymptotic behaviour of random dynamical systems in Polish spaces is considered. Under the assumption of existence of a random compact absorbing set, assumption supposed to hold path by path, a candidate pathwise attractorA(ω) is defined. The goal of the paper is to show that, in the case of stationary dynamical systems,A(ω) attracts bounded sets, is measurable with respect to the σ-algebra of invariant sets, and is independent of ω when the system is ergodic. An application to a general class of Navier-Stokes type equations perturbed by a multiplicative ergodic real noise is discussed in detail.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Jagiellonian University, Kraków, Poland

    Zdzislaw Brzeźniak & Marek Capiński

  2. Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56100, Pisa, Italy

    Franco Flandoli

Authors
  1. Zdzislaw Brzeźniak
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  2. Marek Capiński
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  3. Franco Flandoli
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Brzeźniak, Z., Capiński, M. & Flandoli, F. Pathwise global attractors for stationary random dynamical systems. Probab. Th. Rel. Fields 95, 87–102 (1993). https://doi.org/10.1007/BF01197339

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  • Received: 20 March 1991

  • Revised: 10 June 1992

  • Issue Date: March 1993

  • DOI: https://doi.org/10.1007/BF01197339

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Keywords

  • Dynamical System
  • Stochastic Process
  • Asymptotic Behaviour
  • Probability Theory
  • General Class
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