LÉVY AREA OF WIENER PROCESSES IN BANACH SPACES
LÉVY AREA OF WIENER PROCESSES IN BANACH SPACES
复制标题
Banach 空间中维纳过程的 LÉVY 面积
DOI：
10.1214/aop/1023481002
复制
发表时间：
2002
影响因子：
2.3
通讯作者：
Z. Qian
中科院分区：
文献类型：
--
作者：
M. Ledoux;Terry Lyons;Z. Qian
本文的目标是通过二进近似为 Banach 空间有价值的布朗运动构建规范 Levy 区域过程。正则 Levy 区域过程存在的意义在于，可以为此类布朗运动（在巴纳赫空间中）建立（随机）积分理论。具有无限维噪声的随机微分方程的流的存在性可以通过 Lyons、Lyons 和 Qien 的结果得出[参见，例如，系统控制和粗糙路径 (2000)。牛津大学按]。这项研究涉及对张量范数的选择进行仔细分析，其动机是应用于无限维随机微分方程。
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.