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May 2003 Logarithmic asymptotics for the supremum of a stochastic process
Ken Duffy, John T. Lewis, Wayne G. Sullivan
Ann. Appl. Probab. 13(2): 430-445 (May 2003). DOI: 10.1214/aoap/1050689587


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.


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Ken Duffy. John T. Lewis. Wayne G. Sullivan. "Logarithmic asymptotics for the supremum of a stochastic process." Ann. Appl. Probab. 13 (2) 430 - 445, May 2003.


Published: May 2003
First available in Project Euclid: 18 April 2003

zbMATH: 1032.60025
MathSciNet: MR1970270
Digital Object Identifier: 10.1214/aoap/1050689587

Primary: 60F10
Secondary: 60K25

Keywords: Extrema of stochastic process , large deviation theory , Queueing theory

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.13 • No. 2 • May 2003
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