CONSTRUCTION OF AN EDWARDS' PROBABILITY MEASURE ON C(R+, R)

• 成果类型: Article
• 署名作者: Najnudel, Joseph
• 署名单位: University of Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP540
• 发表日期: 2010
• 页码: 2295-2321
• 关键词: brownian-motion; MODEL

摘要

In this article, we prove that the measures Q(T) associated to the one-dimensional Edwards' model on the interval [0. T] converge to a limit measure Q when T goes to infinity, in the following sense: for all s >= 0 and for all events A(s) depending on the canonical process only up to time s, Q(T) (A(s)) Q(A(s)). Moreover, we prove that, if P is Wiener measure, there exists a martingale (D-s)(s is an element of R+) such that Q(A(s)) = E-P(1(As) D-s), and we give an explicit expression for this martingale.