中文摘要：

有限时滞随机泛函微分方程的存在唯一性已经得到较多的研究，但对于无限时滞随机泛函微分方程的性质极少．本文在不需要线性增长条件，在一致Lipschitz条件下证明了无限时滞中立型随机泛函微分方程的存在唯一性，给出了精确解和近似解的误差估计，最后给出了解的矩估计．

英文摘要：

The existence and uniqueness of stochastic functional differential equation with finite delay has been studied,but there is almost no work on the property of the neutral stochastic functional differential equations with infinite delay,The main aim of this paper is to close this gap. The paper establishes the existence and uniqueness theorem of solutions to the neutral stochastic functional dif- ferential equations with infinite delay（short for INSFDEs） under the uniform Lipschitz condition （the linear growth condition is weaked）, and gives the estimate for the error between approximate solution and accurate solution. Finally,the moment estimate for the solution is obtained.