Frontiers of Mathematics in China

 Front. Math. China    2017, Vol. 12 Issue (4) : 859-877     DOI: 10.1007/s11464-017-0648-x
 RESEARCH ARTICLE |
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. Corresponding Authors: Xi GENG Issue Date: 06 July 2017
 Cite this article: Xi GENG,Zhongmin QIAN. Finite dimensional characteristic functions of Brownian rough path[J]. Front. Math. China, 2017, 12(4): 859-877. URL: http://journal.hep.com.cn/fmc/EN/10.1007/s11464-017-0648-x http://journal.hep.com.cn/fmc/EN/Y2017/V12/I4/859