Logarithmic asymptotics for the supremum of a stochastic process
Duffy, Ken ; Lewis, John T. ; Sullivan, Wayne G.
Ann. Appl. Probab., Tome 13 (2003) no. 1, p. 430-445 / Harvested from Project Euclid
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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.
Publié le : 2003-05-14
Classification:  Extrema of stochastic process,  large deviation theory,  queueing theory,  60F10,  60K25 
@article{1050689587,
     author = {Duffy, Ken and Lewis, John T. and Sullivan, Wayne G.},
     title = {Logarithmic asymptotics for the supremum of a stochastic process},
     journal = {Ann. Appl. Probab.},
     volume = {13},
     number = {1},
     year = {2003},
     pages = { 430-445},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1050689587}
}

Duffy, Ken; Lewis, John T.; Sullivan, Wayne G. Logarithmic asymptotics for the supremum of a stochastic process. Ann. Appl. Probab., Tome 13 (2003) no. 1, pp.  430-445. http://gdmltest.u-ga.fr/item/1050689587/