Finite dimensional characteristic functions of Brownian rough path

doi:10.1007/s11464-017-0648-x

Frontiers of Mathematics in China

2017, Vol. 12

Issue (4): 859-877 https://doi.org/10.1007/s11464-017-0648-x

本期目录

Finite dimensional characteristic functions of Brownian rough path

Xi GENG¹(

), Zhongmin QIAN²

¹. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15217, US
². Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK

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Abstract：

The Brownian rough path is the canonical lifting of Brownian motion to the free nilpotent Lie group of order 2. Equivalently, it is a process taking values in the algebra of Lie polynomials of degree 2, which is described explicitly by the Brownian motion coupled with its area process. The aim of this article is to compute the finite dimensional characteristic functions of the Brownian rough path in $? d$ and obtain an explicit formula for the case when d = 2.

Key words： Brownian rough paths finite dimensional characteristic functions Riccati system

收稿日期: 2015-09-23 出版日期: 2017-07-06

Corresponding Author(s): Xi GENG

引用本文:

. [J]. Frontiers of Mathematics in China, 2017, 12(4): 859-877.
Xi GENG, Zhongmin QIAN. Finite dimensional characteristic functions of Brownian rough path. Front. Math. China, 2017, 12(4): 859-877.

链接本文:

https://academic.hep.com.cn/fmc/CN/10.1007/s11464-017-0648-x
https://academic.hep.com.cn/fmc/CN/Y2017/V12/I4/859

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