Logarithmic asymptotics for the supremum of a stochastic process

• 成果类型: Article
• 署名作者: Duffy, K; Lewis, JT; Sullivan, WG
• 署名单位: Technological University Dublin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2003
• 页码: 430-445
• 关键词: large deviations; QUEUE

摘要

Logarithmic asymptotics are proved for the tail of the supremum of a stochastic process, under the assumption that the process satisfies a restricted large deviation principle on regularly varying scales. The formula for the rate of decay of the tail of the supremum, in terms of the underlying rate function, agrees with that stated by Duffield and O'Connell [Math. Proc. Cambridge Philos. Soc. (1995) 118 363-374]. The rate function of the process is not assumed to be convex. A number of queueing examples are presented which include applications to Gaussian processes and Weibull sojourn sources.