Cramer's estimate for a reflected levy process

• 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: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000016
• 发表日期: 2005
• 页码: 1445-1450
• 关键词: queue

摘要

The natural analogue for a Levy process of Cramer's estimate for a reflected random walk is a statement about the exponential rate of decay of the tail of the characteristic measure of the height of an excursion above the minimum. We establish this estimate for any Levy process with finite negative mean which satisfies Cramer's condition, and give an explicit formula for the limiting constant. Just as in the random walk case, this leads to a Poisson limit theorem for the number of high excursions.