Synchronization by noise for order-preserving random dynamical systems
- Authors: Franco Flandoli, Benjamin Gess, Michael Scheutzow
- Preprint year: 2015
- First public date: 2015-03-30
- arXiv: 1503.08737
- Status: Published
- Publication type: Journal article
- Publication year: 2017
- Journal: The annals of probability, 45 (2017) 2, pp. 1325-1350
- DOI: 10.1214/16-AOP1088
Abstract
We provide sufficient conditions for weak synchronization 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.