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中文摘要：
以无穷时滞随机泛函微分方程为研究对象，通过选取由王克和黄启昌建立的空间Ch为方程的解所在的相空间．解决了时滞项总是贯穿于整个历史阶段的主要困难．在适当的条件下．得到了随机泛函微分方程的解的先验估计；再结合一致Lipschitz条件，通过构造Picard迭代序列，利用Doob鞅不等式、Gronwall不等式、Borel-Cantelli引理及一些基本不等式，得到该方程的解在区间[to，∞）上是存在且唯一的．进一步，得到近似解与精确解之间的误差估计．其中to为正常数．
英文摘要：
The stochastic functional differential equations with infinite delay was considered in this paper, by choosing the space Ch which was built by Wang Ke and Huang Qichang as the phase space,the delay term that it always worked during the whole history for the solution of the system was cancelled. Under some moderate conditions, the prior estimate of the solutions of the system is obtained. Making use of constructing Picard iterative sequence, Doob martingale inequality, Gronwall inequality, Borel-Cantelli !emma and some fundamental inequalities, together with the uniform Lipschitz conditions, the existence and uniqueness of the Solution for stochastic functional differential equations with infinite delay is derived on the interval [to, ∞）. Further, the estimate of the error for the approximate solution and the accurate solution is obtained, where to is a positive number.
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