Asymptotic separation between solutions of Caputo fractional stochastic differential equations

作者：Son, Doan Thai^*; Huong, Phan Thi; Kloeden, Peter E.; Tuan, Hoang The

来源：Stochastic Analysis and Applications, 2018, 36(4): 654-664.

DOI：10.1080/07362994.2018.1440243

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

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.

• 出版日期2018