APPROXIMATIONS OF THE WIENER SAUSAGE AND ITS CURVATURE MEASURES

• 成果类型: Article
• 署名作者: Rataj, Jan; Spodarev, Evgeny; Meschenmoser, Daniel
• 署名单位: Charles University Prague; Ulm University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP596
• 发表日期: 2009
• 页码: 1840-1859
• 关键词: parallel sets

摘要

A parallel neighborhood of a path of a Brownian motion is sometimes called the Wiener sausage. We consider almost sure approximations of this random set by a sequence of random polyconvex sets and show that the convergence of the corresponding mean curvature measures holds under certain conditions in two and three dimensions. Based on these convergence results, the mean curvature measures of the Wiener sausage are calculated numerically by Monte Carlo simulations in two dimensions. The corresponding approximation formulae are given.