The Annals of Probability
- Ann. Probab.
- Volume 30, Number 2 (2002), 546-578.
Lévy area of Wiener processes in Banach spaces
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.
Ann. Probab., Volume 30, Number 2 (2002), 546-578.
First available in Project Euclid: 7 June 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60H15: Stochastic partial differential equations [See also 35R60] 60J60: Diffusion processes [See also 58J65] 60G15: Gaussian processes
Ledoux, M.; Lyons, T.; Qian, Z. Lévy area of Wiener processes in Banach spaces. Ann. Probab. 30 (2002), no. 2, 546--578. doi:10.1214/aop/1023481002. https://projecteuclid.org/euclid.aop/1023481002