The Annals of Applied Probability

Logarithmic asymptotics for the supremum of a stochastic process

Ken Duffy, John T. Lewis, and Wayne G. Sullivan

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 13, Number 2 (2003), 430-445.

Dates
First available in Project Euclid: 18 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1050689587

Digital Object Identifier
doi:10.1214/aoap/1050689587

Mathematical Reviews number (MathSciNet)
MR1970270

Zentralblatt MATH identifier
1032.60025

Subjects
Primary: 60F10: Large deviations
Secondary: 60K25: Queueing theory [See also 68M20, 90B22]

Keywords
Extrema of stochastic process large deviation theory queueing theory

Citation

Duffy, Ken; Lewis, John T.; Sullivan, Wayne G. Logarithmic asymptotics for the supremum of a stochastic process. Ann. Appl. Probab. 13 (2003), no. 2, 430--445. doi:10.1214/aoap/1050689587. https://projecteuclid.org/euclid.aoap/1050689587


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  • RATHMINES, DUBLIN 6 IRELAND E-MAIL: ken.duffy, john.lewis, way ne.sullivan@cnri.dit.ie