The Existence and Uniqueness for the Solution of Neutral Stochastic Functional Differential Equations with Infinite Delay

DOI：10.3770/j.issn:1000-341X.2010.04.003

 作者 单位 陈华斌 南昌大学理学院数学系, 江西 南昌 330033 华中科技大学数学与统计学院, 湖北 武汉 430074

在本文中，我们将用一种新的方法来研究在$BC((-\infty,0];R^d)$内带无限时滞中立型随机泛函微分方程的解的存在唯一性.通过构造一种新的迭代格式,仅在Lipschitz条件,线性增长条件和压缩条件下,我们能直接地得到带无限时滞中立型随机泛函微分方程的解的存在唯一性.同时,我们也能给出解的矩估计以及近似解与精确解之间的误差估计.与已有的结果相比,我们的方法部分地不同于Picard迭代方法,并且补充了一些现有文献的结果.

In this paper, we will make use of a new method to study the existence and uniqueness for the solution of neutral stochastic functional differential equations with infinite delay (INSFDEs for short) in the phase space $BC((-\infty,0];R^d)$. By constructing a new iterative scheme, the existence and uniqueness for the solution of INSFDEs can be directly obtained only under uniform Lipschitz condition, linear grown condition and contractive condition. Meanwhile, the moment estimate of the solution and the estimate for the error between the approximate solution and the accurate solution can be both given. Compared with the previous results, our method is partially different from the Picard iterative method and our results can complement the earlier publications in the existing literatures.