Large deviations for random walks under subexponentiality: The big-jump domain

• 成果类型: Article
• 署名作者: Denisov, D.; Dieker, A. B.; Shneer, V.
• 署名单位: Heriot Watt University; International Business Machines (IBM); IBM USA; Euratom
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP382
• 发表日期: 2008
• 页码: 1946-1991
• 关键词: random-variables; LIMIT-THEOREMS; sums; probabilities; BEHAVIOR

摘要

For a given one-dimensional random walk {S-n} with a subexponential step-size distribution, we present a unifying theory to study the sequences {x(n)} for which P{S-n > x} as n -> infinity uniformly for x >= x(n). We also investigate the stronger local analogue, P{S-n is an element of (x, x + T]} similar to nP{S-1 is an element of (x, x + T]}. Out- theory is self-contained and fits well within classical results on domains of (partial) attraction and local limit theory. When specialized to the most important subclasses of subexponential distributions that have been studied in the literature, we reproduce known theorems and we supplement them with new results.