Asymptotic separation between solutions of Caputo fractional stochastic differential equations

被引：68

作者：

Son, Doan Thai ^{[1
]}

Huong, Phan Thi ^{[2
]}

Kloeden, Peter E. ^{[3
]}

Tuan, Hoang The ^{[1
]}

机构：

[1] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet Rd, Hanoi, Vietnam

[2] Le Quy Don Tech Univ, 236 Hoang Quoc Viet, Hanoi, Vietnam

[3] Huazhong Univ Sci Technol, Sch Math & Stat, Wuhan, Hubei, Peoples R China

来源：

STOCHASTIC ANALYSIS AND APPLICATIONS | 2018年 / 36卷 / 04期

关键词：

Fractional stochastic differential equations; Existence and uniqueness solutions; Temporally weighted norm; Continuous dependence on the initial condition; Asymptotic behavior; Lyapunov exponents;

D O I：

10.1080/07362994.2018.1440243

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using a temporally weighted norm, we first establish a result on the global existence and uniqueness of solutions for Caputo fractional stochastic differential equations of order inline-graphic whose coefficients satisfy a standard Lipschitz condition. For this class of systems, we then show that the asymptotic distance between two distinct solutions is greater than as t for any E > 0. As a consequence, the mean square Lyapunov exponent of an arbitrary non-trivial solution of a bounded linear Caputo fractional stochastic differential equation is always non-negative.

引用

页码：654 / 664

页数：11

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