GAMBLERS RUIN AND THE FIRST EXIT POSITION OF RANDOM-WALK FROM LARGE SPHERES
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/1176988608
发表日期：
1994
页码：
1429-1472
关键词：
摘要：
Let T-r be the first time a sum S-n of nondegenerate i.i.d. random vectors in R(d) leaves the sphere of radius r in some given norm. We characterize, in terms of the distribution of the individual summands, the following probabilistic behavior: S-Tr/parallel to S(Tr)parallel to has no subsequential weak limit supported on a closed half-space. In one dimension, this result solves a very general form of the gambler's ruin problem. We also characterize the existence of degenerate limits and obtain analogous results for triangular arrays along any subsequence r(k) --> infinity. Finally, we compute the limiting joint distribution of (parallel to S(Tr)parallel to - r, S-Tr/parallel to S(Tr)parallel to).
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