SYNCHRONIZATION BY NOISE FOR ORDER-PRESERVING RANDOM DYNAMICAL SYSTEMS

• 成果类型: Article
• 署名作者: Flandoli, Franco; Gess, Benjamin; Scheutzow, Michael
• 署名单位: University of Pisa; Max Planck Society; Technical University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1088
• 发表日期: 2017
• 页码: 1325-1350
• 关键词: porous-media equations; small random perturbations; differential-equations; evolution-equations; invariant-measures; random attractor; stabilization; SPACES; chaos

摘要

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.