Open Access
April 2002 Lévy area of Wiener processes in Banach spaces
M. Ledoux, T. Lyons, Z. Qian
Ann. Probab. 30(2): 546-578 (April 2002). DOI: 10.1214/aop/1023481002


The goal of this paper is to construct canonical Lévy area processes for Banach space valued Brownian motions via dyadic approximations. The significance of the existence of canonical Lévy area processes is that a (stochastic) integration theory can be established for such Brownian motions (in Banach spaces). Existence of flows for stochastic differential equations with infinite dimensional noise then follows via the results of Lyons and Lyons and Qian. This investigation involves a careful analysis on the choice of tensor norms, motivated by the applications to infinite dimensional stochastic differential equations.


Download Citation

M. Ledoux. T. Lyons. Z. Qian. "Lévy area of Wiener processes in Banach spaces." Ann. Probab. 30 (2) 546 - 578, April 2002.


Published: April 2002
First available in Project Euclid: 7 June 2002

zbMATH: 1016.60071
MathSciNet: MR1905851
Digital Object Identifier: 10.1214/aop/1023481002

Primary: 60H10
Secondary: 60G15 , 60H15 , 60J60

Keywords: Brownian motion , Differential equation , Gaussian comparison theorem , Gaussian measure , rough path

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 2 • April 2002
Back to Top