无界延迟随机微分方程一般衰减速度的稳定性(英文)

Stochastic Stabilitywith General Decay Rate for Stochastic Differential Equations with Unbounded Delay

本文用Lyapunov函数技巧对非线性无界延迟随机微分方程建立整体解的存在唯一性定理.利用半鞅收敛定理,研究零解的一般衰减速度的随机稳定性并给出判定定理.

By the Lyapunov function technique,this paper establishes the existence and uniqueness theorem of the global solution of a class of nonlinear stochastic differential equations with unbound- ed delay. By the semimartingale convergence theorem, this paper examines stochastic stability with general decay rate of this global solution and gives some stability criteria.