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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

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

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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

Information

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

Subjects:
Primary: 37B25
Secondary: 37G35, 37H15

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 2 • March 2017
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