Stochastic areas, winding numbers and Hopf fibrations

被引：14

作者：

Baudoin, Fabrice ^{[1
]}

Wang, Jing ^{[2
]}

机构：

[1] Univ Connecticut, Dept Math, Mansfield, PA USA

[2] Univ Illinois, Dept Math, 1409 W Green St, Urbana, IL 61801 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2017年 / 169卷 / 3-4期

关键词：

ATIYAH-SINGER THEOREMS; PROBABILISTIC APPROACH;

D O I：

10.1007/s00440-016-0745-x

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We define and study stochastic areas processes associated with Brownian motions on the complex symmetric spaces and . The characteristic functions of those processes are computed and limit theorems are obtained. In the case , we also study windings of the Brownian motion on those spaces and compute the limit distributions. For the geometry of the Hopf fibration plays a central role, whereas for it is the anti-de Sitter fibration.

引用

页码：977 / 1005

页数：29

共 26 条

[1]

[Anonymous], 1961, Ann. Scuola Norm. Sup. Pisa

[2]

Baudoin F., 2012, ESAIM-PROBAB STAT, V16, P453, DOI DOI 10.1051/PS/2011107

[3] The subelliptic heat kernel on the CR sphere [J].