Logarithmic asymptotics for the supremum of a stochastic process

Duffy, Ken R. and Lewis, John T. and Sullivan, Wayne G. (2003) Logarithmic asymptotics for the supremum of a stochastic process. Annals of Applied Probability, 13 (2). pp. 430-445. ISSN 1050-5164

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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.

Item Type: Article
Keywords: Logarithmic asymptotics; Supremum; Stochastic process; Gaussian processes; Weibull sojourn sources.
Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1823
Identification Number: 10.1214/aoap/1050689587
Depositing User: Hamilton Editor
Date Deposited: 01 Feb 2010 18:24
Journal or Publication Title: Annals of Applied Probability
Publisher: Institute of Mathematical Statistics
Refereed: Yes

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