Asymptotic separation between solutions of Caputo fractional stochastic differential equations

By Doan Thai Son, Phan Thi Huong, Peter E. Kloeden, Hoang The Tuan. 2017

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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.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

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