Lévy area of Wiener processes in Banach spaces

Lévy area of Wiener processes in Banach spaces

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

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

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.

Primary Subjects: 60H10

Secondary Subjects: 60H15, 60J60, 60G15

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

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1023481002
Mathematical Reviews number (MathSciNet): MR1905851
Digital Object Identifier: doi:10.1214/aop/1023481002
Zentralblatt MATH identifier: 1016.60071

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