中文摘要：

证明了一个用二次连续可导函数来逼近二阶导数存在有限个第一类不连续点的连续可导函数的结论，并用这个结论推广了广泛应用于随机控制模型研究中的一个随机分析结论，给某些重要随机控制模型的推广提供了关键性的理论工具．

英文摘要：

In this paper, the theorem 2 proves a conclusion that we can construct a series of twice con- tinuously differentiable functions to approximate a continuously differentiable function whose second order derived function has only finite discontinuity points of the first kind. Applying this conclusion, this paper generalizes a stochastic analysis conclusion which is used in the researches of stochastic con- trol models extensively. This generalized conclusion provides a key theoretical tool for the development of some important stochastic control models.