ON THE DISTRIBUTION OF BUBBLES OF THE BROWNIAN SHEET
成果类型：
Article
署名作者：
KHOSHNEVISAN, D
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176988290
发表日期：
1995
页码：
786-805
关键词：
摘要：
Let W be a real-valued, two-parameter Brownian sheet. Let us define N(t; h) to be the total number of bubbles of W in [0, t](2), whose maximum height is greater than h. Evidently, lim(h down arrow 0) N(t; h) = infinity and lim(t) (up arrow) (infinity) N(t; h) = infinity. It is the goal of this paper to provide fairly accurate estimates on N(t; h) both as t --> infinity and as h --> 0. Loosely speaking, we show that there are of order h(-3) many such bubbles as h down arrow 0 and t(3) many, as t up arrow infinity.