Setvalued Dynamical Systems for Stochastic Evolution Equations Driven by Fractional Noise

被引：7

作者：

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

Schmalfuss, B. ^{[2
]}

Valero, J. ^{[3
]}

机构：

[1] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, Avda Reina Mercedes S-N, Seville 41012, Spain

[2] Friedrich Schiller Univ Jena, Inst Stochast, Ernst Abbe Pl 2, D-77043 Jena, Germany

[3] Univ Miguel Hernandez, Ctr Invest Operat, Avda Univ S-N, Elche 03202, Spain

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2022年 / 34卷 / 01期

关键词：

Fractional Brownian motion; Fractional derivatives; Multivalued random dynamical systems; RANDOM ATTRACTORS; BROWNIAN-MOTION;

D O I：

10.1007/s10884-019-09811-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider Hilbert-valued evolution equations driven by Holder paths with Holder index greater than 1/2, which includes the case of fractional noises with Hurst parameters in (1/2,1). The assumptions of the drift term will not be enough to ensure the uniqueness of solutions. Nevertheless, adopting a multivalued setting, we will prove that the set of all solutions corresponding to the same initial condition generates a (multivalued) nonautonomous dynamical system phi is measurable (and hence a (multivalued) random dynamical system), we need to construct a new metric dynamical system that models the noise with the property that the set space is separable.

引用

页码：79 / 105

页数：27

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