Levy area of Wiener processes in Banach spaces

• 成果类型: Article
• 署名作者: Ledoux, M; Lyons, T; Qian, Z
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Oxford
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2002
• 页码: 546-578
• 关键词: differential-equations; brownian-motion

摘要

The goal of this paper is to construct canonical Levy area processes for Banach space valued Brownian motions via dyadic approximations. The significance of the existence of canonical Levy 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 [see, e.g., System Control and Rough Paths (2000). Oxford Univ. Press]. This investigation involves a careful analysis on the choice of tensor norms, motivated by the applications to infinite dimensional stochastic differential equations.