Asymptotic separation between solutions of Caputo fractional stochastic differential equations

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 \(\alpha\in(\frac{1}{2},1)\) whose coefficients satisfy a standard Lipschitz condition. For this class of systems we then...

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Bibliographic Details
Published in:arXiv.org 2017-11
Main Authors: Doan, T S, Huong, P T, Kloeden, P E, Tuan, H T
Format: Article
Language:English
Subjects:
Asymptotic properties
Differential equations
Lipschitz condition
Mathematical analysis
Online Access:Get full text
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Summary: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 \(\alpha\in(\frac{1}{2},1)\) 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 \(t^{-\frac{1-\alpha}{2\alpha}-\eps}\) as \(t \to \infty\) for any \(\eps>0\). 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1711.08622