INEQUALITIES FOR THE OVERSHOOT
成果类型：
Article
署名作者：
Chang, Joseph T.
署名单位：
Yale University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004913
发表日期：
1994
页码：
1223-1233
关键词：
摘要：
Let X-1, X-2, ... be independent and identically distributed positive random variables with S-n = X-1 + ... +X-n, and for nonnegative b define R-b = inf{S-n - b: S-n > b}. Then R-b is called the overshoot at b. In terms of the moments of X-1, Lorden gave bounds for the moments of R-b that hold uniformly over all b. Using a coupling argument, we establish stochastic ordering inequalities that imply the moment inequalities of Lorden. In addition to simple new proofs of Lorden's inequalities, we provide new inequalities for the tail probabilities P{R-b > x} and moments of R-b that improve upon those of Lorden. We also present conjectures for sharp moment inequalities and describe an application to the first ladder height of random walks.
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