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
DOI: 10.1214/16-AOP1088
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Resumen
- 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.