Asymptotic separation between solutions of Caputo fractional stochastic differential equations. Issue 4 (4th July 2018)

• Record Type: Journal Article
• Authors: Son, Doan Thai; Huong, Phan Thi; Kloeden, Peter E.; Tuan, Hoang The
• Is Part Of: Stochastic analysis and applications. Volume 36:Issue 4(2018)
• Page Start: 654
• Page End: 664
• Publication Date: 2018-07-04
• Subjects: Fractional stochastic differential equations -- Existence and uniqueness solutions -- Temporally weighted norm -- Continuous dependence on the initial condition -- Asymptotic behavior, Lyapunov exponents; 26A33, 34A08, 34A12, 34D05 Secondary: 60H10; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2018.1440243
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: 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 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 ϵ > 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.