布朗运动对应的狄氏型及其变换  

Dirichlet Forms Corresponding to Brownian Motion and Their Transformation

作　　者：孟进 张静[1] MENG Jin;ZHANG Jing(School of Mathematics and Statistics,Hainan Normal University,Haikou 571158,China)

机构地区：[1]海南师范大学数学与统计学院,海南海口571158

出　　处：《海南师范大学学报（自然科学版）》2021年第1期21-26,共6页Journal of Hainan Normal University（Natural Science）

基　　金：国家自然科学基金项目(11701127;11871184)。

摘　　要：首先根据马氏过程的半群与生成元之间的关系,通过泰勒展开式等运算得到布朗运动的生成元的表达式,再利用生成元与二次型的关系式得到布朗运动所对应的狄氏型的表达式;然后以布朗运动对应的狄氏型为基本型考虑两类变换:变换一保持参考测度不变,改变基本型;变换二保持基本型不变,改变参考测度。最后找到变换前后狄氏型的拟正则性保持不变的条件。Firstly,according to the relationship between the semigroup and the generator of Markov process,the generator expression of Brownian motion was obtained by Taylor expansion and other operations.Secondly,the Dirichlet form corresponding to Brownian motion was obtained by using the relation between generator and quadratic form.Finally,the Dirichlet form corresponding to Brownian motion was taken as the basic type,and two kinds of transformations were considered,one is to keep the reference measure unchanged and change the basic type,the other is to keep the basic type unchanged and change the reference measure.Finally,the condition that the quasi-regularity of Dirichlet forms remains unchanged before and after the transformation was also found.

关 键 词：布朗运动 狄氏型 拟正则性 变换 

分 类 号：O211.62[理学—概率论与数理统计]