Synchronization by noise for order-preserving random dynamical systems | Zendy

Franco Flandoli | Zendy; Benjamin Gess | Zendy; Michael Scheutzow | Zendy

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Synchronization by noise for order-preserving random dynamical systems

Author(s) -

Franco Flandoli,

Benjamin Gess,

Michael Scheutzow

Publication year - 2017

Publication title -

the annals of probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.184

H-Index - 98

eISSN - 2168-894X

pISSN - 0091-1798

DOI - 10.1214/16-aop1088

Subject(s) - mathematics , attractor , synchronization (alternating current) , banach space , noise (video) , random dynamical system , order (exchange) , dynamical systems theory , point (geometry) , point process , fixed point , pure mathematics , mathematical analysis , topology (electrical circuits) , linear dynamical system , combinatorics , linear system , computer science , statistics , physics , geometry , finance , quantum mechanics , artificial intelligence , economics , image (mathematics)

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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