The Levy area process for the free Brownian motion

Authors
Capitaine, M Donati-Martin, C
Citation
M. Capitaine et C. Donati-martin, The Levy area process for the free Brownian motion, J FUNCT ANA, 179(1), 2001, pp. 153-169
Citations number
10
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF FUNCTIONAL ANALYSIS
ISSN journal
00221236 → ACNP
Volume
179
Issue
1
Year of publication
2001
Pages
153 - 169
Database
ISI
SICI code
0022-1236(20010110)179:1<153:TLAPFT>2.0.ZU;2-N
Abstract
In this paper, we construct a Levy area process for the free Brownian motio n and in this way, a typical geometric rough path (in the sense of T. Lyons (1998, Rev. Mat. Iberoamer. 14, 215-310)), lying above the free Brownian p ath. Thus, the general results of Lyons on differential equations driven by rough paths may be applied to the free Brownian motion case. (C) 2001 Acad emic Press.