无限时滞的随机泛函微分方程解的渐近性质

摘要

In this paper, the existence and uniqueness and moment boundedness of solutions to stochastic functional differential equations with infinite delay are studied. By using the method of Lyapunov functions and the introduction of probability measures, a new condition which assures that the equations have a unique solution and at the same time the moment boundedness, the moment average in time boundedness of this solution is obtained. Relevant results about the Khasminskii-Mao theorems are generalized.%本文研究了无限时滞随机泛函微分方程解的存在唯一性,矩有界性的问题.利用Lyapunov函数法以及概率测度的引入得到了确保方程解在唯一、矩有界、时间平均矩有界同时成立的一个新的条件.推广了Khasminskii-Mao定理的相关结果.