Synchronization by noise for order-preserving random dynamical systems

• Franco Flandoli ^[1] ; Benjamin Gess ^[2] ; Michael Scheutzow ^[3]
  1. [1] University of Pisa

     University of Pisa

     Pisa, Italia

     
  2. [2] Max Planck Institute for Mathematics in the Sciences

     Max Planck Institute for Mathematics in the Sciences

     Kreisfreie Stadt Leipzig, Alemania

     
  3. [3] Technical University of Berlin

     Technical University of Berlin

     Berlin, Stadt, Alemania

     

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 2, 2017, págs. 1325-1350
• Idioma: inglés
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  • We provide sufficient conditions for weak synchronization/stabilization by noise for order-preserving random dynamical systems on Polish spaces. That is, under these conditions we prove the existence of a weak point attractor consisting of a single random point. This generalizes previous results in two directions: First, we do not restrict to Banach spaces, and second, we do not require the partial order to be admissible nor normal. As a second main result and application, we prove weak synchronization by noise for stochastic porous media equations with additive noise.