INTERSECTION LOCAL-TIMES FOR INFINITE SYSTEMS OF BROWNIAN MOTIONS AND FOR THE BROWNIAN DENSITY PROCESS

• 成果类型: Article
• 署名作者: ADLER, RJ; FELDMAN, RE; LEWIN, M
• 署名单位: University of California System; University of California Berkeley; University of California System; University of California Santa Barbara
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990540
• 发表日期: 1991
• 页码: 192-220
• 关键词: limit-theorems

摘要

The Brownian density process is a distribution-valued process that arises either via a limiting operation on an infinite collection of Brownian motions or as the solution of a stochastic partial differential equation. It has a (self-) intersection local time, that is formally defined through an operation involving delta functions, much akin to the better studied intersection local time of measure-valued (super) processes. Our main aim is to show that this formal definition not only makes sense mathematically, but can also be understood, at least in two and three dimensions, via the intersection local times of simple Brownian motions. To show how useful this way of looking at the Brownian density intersection local time can be, we also derive a Tanaka-like evolution equation for it in the two-dimensional case.