本文使用Malliavin分析的方法,研究由带漂移项的Kohn-Laplace型算子生成的扩散过程的导数公式,推广了V=0情形的结果.本文主要分为三部分:第一部分介绍有关研究背景, 包括关于亚椭圆型扩散半群的有关研究,导数公式及应用. 第二部分主要介绍已有的未加漂移项的Kohn-Laplace型算子生成的扩散过程的导数公式. 第三部分对第二部分结果进行推广,建立了添加了漂移项后的Kohn-Laplace型算子生成的扩散过程的导数公式.

By using Malliavin Calculus, we study the Bismut-typederivative formula of the diffusion processes generated by Kohn-Laplacian type operators.This work consists of three chapters as follows.The first part introduces the background of the studies of sub-elliptic diffusion semigroups. In the second part, we introduce the results in about the derivative formulas generated by the Kohn-Laplacian type operators. The third part, which is thegeneralization of the second part, is the derivative formulas of the diffusion processes generated by the Kohn-Laplacian type operatorswith drift.