Passage times of random walks and Levy processes across power law boundaries
成果类型：
Article
署名作者：
Doney, RA; Maller, RA
署名单位：
University of Manchester; Australian National University; Australian National University
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-004-0414-3
发表日期：
2005
页码：
57-70
关键词：
摘要：
We establish an integral test involving only the distribution of the increments of a random walk S which determines whether lim sup(n-->infinity() S-n/n(k)) is almost surely zero, finite or infinite when 1/2 < k < 1 and a typical step in the random walk has zero mean. This completes the results of Kesten and Maller [9] concerning finiteness of one-sided passage times over power law boundaries, so that we now have quite explicit criteria for all values of k >= 0. The results, and those of [9], are also extended to Levy processes.
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