中文摘要：

首先介绍随机微分方程基本理论，然后基于我国上证综合指数的离散观测数据，运用非参数方法对随机微分方程的漂移项和扩散项进行估计．核函数的方法用来近似估计随机过程中期望函数，从而得到了漂移项和扩散项的非参数估计．相比于参数估计方法，非参数方法是一种使用尽可能少的假设但又能通过数据推测未知的数量特征的方法，它是一种无限维的方法，因而显得更为灵活、适应性更广和更具发展潜力．最后，运用统计软件R语言对其进行实证分析．

英文摘要：

In recent ten years, nonparametric techniques are applied to estimate the drift term and the diffusion term of stochastic differential equations, and many related results perform well. In this article, we first introduce the essential theory of stochastic differential equations. Kernel smoothing approach is applied to estimate the ex- pectation function of the stochastic processes, then the nonparametric estimation of drift term and diffusion term is obtained. Compared with parametric methods, nonparametric methods depend on least assumptions while ex- ploring the characteristics of some unknown terms based on the observed data. It is an infinite dimensional method, which is more flexible, more adaptive and more potential. Finally, we do some statistical inference based on the data from the Shanghai Composite Index. R software is used to carry out this analysis.