CONDITIONAL LIMIT THEOREMS FOR REGULATED FRACTIONAL BROWNIAN MOTION

• 成果类型: Article
• 署名作者: Awad, Hernan; Glynn, Peter
• 署名单位: University of Miami; Stanford University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP605
• 发表日期: 2009
• 页码: 2102-2136
• 关键词: large deviations; Moderate Deviations; Self-similarity; levy motion; QUEUE; extremes; tails

摘要

We consider a stationary fluid queue with fractional Brownian motion input. Conditional on the workload at time zero being greater than a large value b, we provide the limiting distribution for the amount of time that the workload process spends above level b over the busy cycle straddling the origin, as b -> infinity. Our results can be interpreted as showing that long delays occur in large clumps of size of order b(2-1/H). The conditional limit result involves a finer scaling of the queueing process than fluid analysis, thereby departing from previous related literature.