RANDOM DYNAMICAL SYSTEMS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION

被引：66

作者：

Garrido-Atienza, Maria J. ^{[1
]}

Lu, Kening ^{[2
]}

Schmalfuss, Bjoern ^{[3
]}

机构：

[1] Univ Seville, Dpto Ecuac Diferenciales & Anal Numer, E-41080 Seville, Spain

[2] 346 TMCB Brigham Young Univ, Provo, UT 84602 USA

[3] Univ Paderborn, Inst Math, Fak EIM, D-33098 Paderborn, Germany

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2010年 / 14卷 / 02期

基金：

美国国家科学基金会;

关键词：

Stochastic PDEs; fractional Brownian motion; random dynamical systems; EVOLUTION-EQUATIONS; STATIONARY SOLUTIONS; SPDES;

D O I：

10.3934/dcdsb.2010.14.473

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study nonlinear stochastic partial differential equations (SPDEs) driven by a fractional Brownian motion (fBm) with the Hurst parameter bigger than 1/2. We show that these SPDEs generate random dynamical systems (or stochastic flows) by using the stochastic calculus for an fBm where the stochastic integrals are defined by integrands given by fractional derivatives. In particular, we emphasize that the coefficients in front of the fractional noise are non-trivial.

引用

页码：473 / 493

页数：21

共 25 条

[1]

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

[2] Exponentially stable stationary solutions for stochastic evolution equations and their perturbation [J].

Caraballo, T ;

Kloeden, PE ;

Schmalfuss, B .

APPLIED MATHEMATICS AND OPTIMIZATION, 2004, 50 (03) :183-207

[3]

CARABALLO T, DISCRETE CO IN PRESS

[4]

Castaing C., 1977, CONVEX ANAL MEASURAB, V580, DOI DOI 10.1007/BFB0087686

[5] Stochastic analysis of the fractional Brownian motion [J].

Decreusefond, L ;

Üstünel, AS .

POTENTIAL ANALYSIS, 1999, 10 (02) :177-214

[6]

Duan J., 2004, J DYNAM DIFFERENTIAL, V16, P949

[7]

Duan JQ, 2003, ANN PROBAB, V31, P2109

[8] Stationary conjugation of flows for parabolic SPDEs with multiplicative noise and some applications [J].

Flandoli, F ;

Lisei, H .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2004, 22 (06) :1385-1420

[9] Unstable invariant manifolds for stochastic PDEs driven by a fractional Brownian motion [J].

Garrido-Atienza, Maria J. ;

Lu, Kening ;

Schmalfuss, Bjoern .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (07) :1637-1667

[10]

GARRIDOATIENZA MJ, INT J BIFUR IN PRESS

← 1 2 3 →