A note on the generation of random dynamical systems from fractional stochastic delay differential equations

被引：4

作者：

Luu Hoang Duc ^{[1
,2
,3
]}

Schmalfuss, Bjoern ^{[4
]}

Siegmund, Stefan ^{[2
,3
]}

机构：

[1] Vietnam Acad Sci & Technol, Inst Math, Hanoi 10307, Vietnam

[2] Tech Univ Dresden, Inst Anal, Dresden, Germany

[3] Tech Univ Dresden, Ctr Dynam, D-01069 Dresden, Germany

[4] Univ Jena, Inst Stochast, D-77043 Jena, Germany

来源：

STOCHASTICS AND DYNAMICS | 2015年 / 15卷 / 03期

关键词：

Fractional Brownian motion; stochastic differential equations; stochastic delay differential equations; stochastic functional differential equations; ROUGH PATH-ANALYSIS; BROWNIAN-MOTION; EVOLUTION-EQUATIONS; DRIVEN; INTEGRATION; CALCULUS;

D O I：

10.1142/S0219493715500185

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：

In this note we prove that a fractional stochastic delay differential equation which satisfies natural regularity conditions generates a continuous random dynamical system on a subspace of a Holder space which is separable.

引用

页数：13

共 50 条

[41] APPROXIMATION OF SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH FRACTIONAL BROWNIAN MOTION BY SOLUTIONS OF RANDOM ORDINARY DIFFERENTIAL EQUATIONS
Ral'chenko, K. V.
Shevchenko, H. M.
UKRAINIAN MATHEMATICAL JOURNAL, 2011, 62 (09) : 1460 - 1475
[42] Setvalued Dynamical Systems for Stochastic Evolution Equations Driven by Fractional Noise
Garrido-Atienza, M. J.
Schmalfuss, B.
Valero, J.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2022, 34 (01) : 79 - 105
[43] Setvalued Dynamical Systems for Stochastic Evolution Equations Driven by Fractional Noise
M. J. Garrido-Atienza
B. Schmalfuss
J. Valero
Journal of Dynamics and Differential Equations, 2022, 34 : 79 - 105
[44] Controllability of fractional stochastic delay equations
Ahmed H.M.
Lobachevskii Journal of Mathematics, 2009, 30 (3) : 195 - 202
[45] A DYNAMICAL THEORY FOR SINGULAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS II: NONLINEAR EQUATIONS AND INVARIANT MANIFOLDS
Varzaneh, Mazyar Ghani
Riedel, Sebastian
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2021, 26 (08): : 4587 - 4612
[46] Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay
Abouagwa, Mahmoud
Bantan, Rashad A. R.
Almutiry, Waleed
Khalaf, Anas D.
Elgarhy, Mohammed
FRACTAL AND FRACTIONAL, 2021, 5 (04)
[47] EULER SCHEME FOR FRACTIONAL DELAY STOCHASTIC DIFFERENTIAL EQUATIONS BY ROUGH PATHS TECHNIQUES
Garzon, Johanna
Tindel, Samy
Torres, Soledad
ACTA MATHEMATICA SCIENTIA, 2019, 39 (03) : 747 - 763
[48] Finite time stability analysis for fractional stochastic neutral delay differential equations
Asadzade, Javad A.
Mahmudov, Nazim I.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2024, 70 (06) : 5293 - 5317
[49] LONG TIME BEHAVIOR OF FRACTIONAL IMPULSIVE STOCHASTIC DIFFERENTIAL EQUATIONS WITH INFINITE DELAY
Xu, Jiaohui
Caraballo, Tomas
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (06): : 2719 - 2743
[50] Averaging Principle for ?-Capuo Fractional Stochastic Delay Differential Equations with Poisson Jumps
Yang, Dandan
Wang, Jingfeng
Bai, Chuanzhi
SYMMETRY-BASEL, 2023, 15 (07):

← 1 2 3 4 5 →