Stable processes have thorns

• 成果类型: Article
• 署名作者: Burdzy, K; Kulczycki, T
• 署名单位: University of Washington; University of Washington Seattle; Polish Academy of Sciences; Wroclaw University of Science & Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 170-194
• 关键词: brownian-motion; points; cones

摘要

Let X(t) be the symmetric alpha-stable process in R-d, alpha is an element of (0, 2), d greater than or equal to 2. For f:(0, 1) --> (0, infinity) let D (f) be the thorn {x is an element of R-d : x(1) is an element of (0, 1), \(x(2), - - -, x(d))\ < f (x(1))}. We give an integral criterion in terms of f for the existence of a random time s such that X(t) remains in X(s) + (D) over bar (f) for all t is an element of [s, s + 1).