Open Access
Translator Disclaimer
March 2017 Synchronization by noise for order-preserving random dynamical systems
Franco Flandoli, Benjamin Gess, Michael Scheutzow
Ann. Probab. 45(2): 1325-1350 (March 2017). DOI: 10.1214/16-AOP1088


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.


Download Citation

Franco Flandoli. Benjamin Gess. Michael Scheutzow. "Synchronization by noise for order-preserving random dynamical systems." Ann. Probab. 45 (2) 1325 - 1350, March 2017.


Received: 1 March 2015; Revised: 1 January 2016; Published: March 2017
First available in Project Euclid: 31 March 2017

zbMATH: 1379.37101
MathSciNet: MR3630300
Digital Object Identifier: 10.1214/16-AOP1088

Primary: 37B25
Secondary: 37G35 , 37H15

Keywords: order-preserving RDS , random attractor , Random dynamical system , statistical equilibrium , Stochastic differential equation , synchronization

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 2 • March 2017
Back to Top