ON THE POSITION OF A RANDOM-WALK AT THE TIME OF 1ST EXIT FROM A SPHERE
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/1176989808
发表日期：
1992
页码：
825-854
关键词：
摘要：
Let T(r) be the first time a sum S(n) of nondegenerate i.i.d. random vectors leaves the sphere of radius r. The spheres are determined by some given norm on R(d) which need not be the Euclidean norm. As a particular case of our results, we obtain, for mean-zero random vectors and each 0 < p < infinity and 0 less-than-or-equal-to q < infinity, necessary and sufficient conditions on the distribution of the summands to have E(parallel-to S(T(r))parallel-to - r)P = O(r(q)) as r --> infinity. We also characterize tightness of the family {parallel-to S(T(r))parallel-to - r} and obtain other related results on the rate of growth of parallel-to S(T(r))parallel-to. In particular, we obtain a simple necessary and sufficient condition for parallel-to S(T(r))parallel-to/r --> p 1.