The Annals of Probability

Synchronization by noise for order-preserving random dynamical systems

Franco Flandoli, Benjamin Gess, and Michael Scheutzow

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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.

Article information

Ann. Probab., Volume 45, Number 2 (2017), 1325-1350.

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

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Zentralblatt MATH identifier

Primary: 37B25: Lyapunov functions and stability; attractors, repellers
Secondary: 37G35: Attractors and their bifurcations 37H15: Multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx]

Synchronization random dynamical system random attractor order-preserving RDS stochastic differential equation statistical equilibrium


Flandoli, Franco; Gess, Benjamin; Scheutzow, Michael. Synchronization by noise for order-preserving random dynamical systems. Ann. Probab. 45 (2017), no. 2, 1325--1350. doi:10.1214/16-AOP1088.

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