Synchronization by noise

被引：45

作者：

Flandoli, Franco ^{[1
]}

Gess, Benjamin ^{[2
]}

Scheutzow, Michael ^{[3
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

[2] Max Planck Inst Math Sci, D-04103 Leipzig, Germany

[3] Tech Univ Berlin, Inst Math, MA 7-5, D-10623 Berlin, Germany

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2017年 / 168卷 / 3-4期

关键词：

Synchronization; Random dynamical system; Random attractor; Lyapunov exponent; Stochastic differential equation; Statistical equilibrium; DYNAMICAL-SYSTEMS; ATTRACTORS; STABILIZATION;

D O I：

10.1007/s00440-016-0716-2

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 synchronization by noise, i.e. under these conditions we prove that weak random attractors for random dynamical systems consist of single random points. In the case of SDE with additive noise, these conditions are also essentially necessary. In addition, we provide sufficient conditions for the existence of a minimal weak point random attractor consisting of a single random point. As a result, synchronization by noise is proven for a large class of SDE with additive noise. In particular, we prove that the random attractor for an SDE with drift given by a (multidimensional) double-well potential and additive noise consists of a single random point. All examples treated in Tearne (Probab Theory Relat Fields 141(1-2):1-18, 2008) are also included.

引用

页码：511 / 556

页数：46

共 49 条

[1]

[Anonymous], 1998, RANDOM DYNAMICAL SYS, DOI DOI 10.1007/978-3-662-12878-7

[2]

[Anonymous], 1991, Spatial Stochastic Processes, DOI DOI 10.1007/978-1-4612-0451-0_9

[3]

[Anonymous], 2002, LECT NOTES MATH

[4] Order-preserving random dynamical systems: Equilibria, attractors, applications [J].

Arnold, L ;

Chueshov, I .

DYNAMICS AND STABILITY OF SYSTEMS, 1998, 13 (03) :265-280

[5]

ARNOLD L, 1983, SIAM J CONTROL OPTIM, V21, P451, DOI 10.1137/0321027

[6]

Arnold L., 1987, Stochastics, V21, P41, DOI 10.1080/17442508708833450

[7] Stabilisation of linear PDES, by Stratonovich noise [J].

Caraballo, T ;

Robinson, JC .

SYSTEMS & CONTROL LETTERS, 2004, 53 (01) :41-50

[8] Synchronization of a stochastic reaction-diffusion system on a thin two-layer domain [J].

Caraballo, Tomas ;

Chueshov, Igor D. ;

Kloeden, Peter E. .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2007, 38 (05) :1489-1507

[9] The effect of noise on the Chafee-Infante equation: A nonlinear case study [J].

Caraballo, Tomas ;

Crauel, Hans ;

Langa, Jose A. ;

Robinson, James C. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (02) :373-382

[10]

Carverhill A., 1985, Stochastics, V14, P273, DOI 10.1080/17442508508833343

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