The Annals of Probability

Lévy area of Wiener processes in Banach spaces

M. Ledoux, T. Lyons, and Z. Qian

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Abstract

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.

Article information

Source
Ann. Probab., Volume 30, Number 2 (2002), 546-578.

Dates
First available in Project Euclid: 7 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1023481002

Digital Object Identifier
doi:10.1214/aop/1023481002

Mathematical Reviews number (MathSciNet)
MR1905851

Zentralblatt MATH identifier
1016.60071

Subjects
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

Keywords
Brownian motion differential equation Gaussian comparison theorem Gaussian measure rough path

Citation

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


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