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

页码：1325 / 1350

页数：26

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