| 孟 进，张 静*.布朗运动对应的狄氏型及其变换[J].海南师范大学学报自科版,2021,34(1):21-26 |
| 布朗运动对应的狄氏型及其变换 |
| Dirichlet Forms Corresponding to Brownian Motion and TheirTransformation |
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| DOI：10.12051/j.issn.1674-4942.2021.01.004 |
| 中文关键词: 布朗运动 狄氏型 拟正则性 变换 |
| 英文关键词: Brownian motion Dirichlet forms quasi-regularity transformation |
| 基金项目:国家自然科学基金项目（11701127；11871184） |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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 corre‐
sponding to Brownian motion was obtained by using the relation between generator and quadratic form. Finally, the Dirich‐
let 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 be‐
fore and after the transformation was also found. |
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