L(p)-boundedness of the overshoot in multidimensional, renewal theory
成果类型：
Article
署名作者：
Griffin, PS; McConnell, TR
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176987814
发表日期：
1995
页码：
2022-2056
关键词：
摘要：
Let T-r be the first time a sum S-n of nondegenerate i.i.d. random variables leaves a ball of radius r in some given norm on R(d). In the case of the Euclidean norm we completely characterize LP-boundedness of the overshoot parallel to S(Tr)parallel to - r in terms of the underlying distribution. For more general norms we provide a similar characterization under a smoothness condition on the norm which is shown to be very nearly sharp. One of the key steps in doing this is a characterization of the possible limit laws of S-Tr/parallel to S(Tr)parallel to under the weaker condition parallel to S(Tr)parallel to/r-->(p) 1.