Abstract
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.
Citation
Franco Flandoli. Benjamin Gess. Michael Scheutzow. "Synchronization by noise for order-preserving random dynamical systems." Ann. Probab. 45 (2) 1325 - 1350, March 2017. https://doi.org/10.1214/16-AOP1088
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