Stochastic bounds for Levy processes

• 成果类型: Article
• 署名作者: Doney, RA
• 署名单位: University of Manchester
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000315
• 发表日期: 2004
• 页码: 1545-1552
• 关键词: random-walks; BOUNDARIES; INFINITY

摘要

Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Levy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Levy process versions of many known results about the large-time behavior of random walks. This is illustrated by establishing a comprehensive theorem about Levy processes which converge to infinity in probability.