SYNCHRONIZATION BY NOISE FOR ORDER-PRESERVING RANDOM DYNAMICAL SYSTEMS

被引：21
|
作者：
Flandoli, Franco [3 ]
Gess, Benjamin [1 ]
Scheutzow, Michael [2 ]
机构：
[1] Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany
[2] Tech Univ Berlin, Inst Matemat, MA 7-5, D-10623 Berlin, Germany
[3] Dipartimento Matemat, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy
来源：
ANNALS OF PROBABILITY | 2017年 / 45卷 / 02期
关键词：
Synchronization; random dynamical system; random attractor; order-preserving RDS; stochastic differential equation; statistical equilibrium; POROUS-MEDIA EQUATIONS; SMALL RANDOM PERTURBATIONS; DIFFERENTIAL-EQUATIONS; EVOLUTION-EQUATIONS; INVARIANT-MEASURES; RANDOM ATTRACTOR; STABILIZATION; SPACES; CHAOS;
D O I：
10.1214/16-AOP1088
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
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.
引用
收藏
页码：1325 / 1350
页数：26
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