Synchronization by noise for order-preserving random dynamical systems

Franco Flandoli; Benjamin Gess; Michael Scheutzow

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arXiv · 1503.08737

Synchronization by noise for order-preserving random dynamical systems

Franco Flandoli·Benjamin Gess·Michael Scheutzow

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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.

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Franco Flandoli, Benjamin Gess, Michael Scheutzow. 2015-03-30. Synchronization by noise for order-preserving random dynamical systems. https://arxiv.org/abs/1503.08737

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