Symmetric stable processes stay in thick sets
成果类型：
Article
署名作者：
Wu, JM
署名单位：
University of Illinois System; University of Illinois Urbana-Champaign
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1078415837
发表日期：
2004
页码：
315-336
关键词：
摘要：
Let X (t) be the symmetric alpha-stable process in R-d (0 < alpha < 2, d greater than or equal to 2). Then let W(f) be the thorn {x is an element of R-d:0 < x(1) < 1, (x(2)(2) +... + x(d)(2))(1)/(2) < f(x(1))} where f : (0, 1) --> (0, 1) is continuous, increasing with f (0(+)) = 0. Recently Burdzy and Kulczycki gave an exact integral condition on f for the existence of a random time s such that X(t) remains in the thorn X(s) + W(f) for all t is an element of [s, s + 1). We extend their theorem to general open sets W with 0 is an element of partial derivativeW. In general, alpha-processes may stay in sets which are quite lacunary and are not locally connected at 0.
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