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arXiv · 1711.08622

Asymptotic separation between solutions of Caputo fractional stochastic differential equations

T. S. Doan·P. T. Huong·P. E. Kloeden·H. T. Tuan
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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 $\alpha\in(\frac{1}{2},1)$ 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.

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T. S. Doan, P. T. Huong, P. E. Kloeden, H. T. Tuan. 2017-11-23. Asymptotic separation between solutions of Caputo fractional stochastic differential equations. https://doi.org/10.1080/07362994.2018.1440243

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