The large deviation principle for the on-off Weibull sojourn process

The large deviation principle for the on-off Weibull sojourn process

Ken R. Duffy and Artem Sapozhnikov

Source: J. Appl. Probab. Volume 45, Number 1 (2008), 107-117.

Abstract

This article proves that the on-off renewal process with Weibull sojourn times satisfies the large deviation principle on a nonlinear scale. Unusually, its rate function is not convex. Apart from on a compact set, the rate function is infinite, which enables us to construct natural processes that satisfy the large deviation principle with nontrivial rate functions on more than one time scale.

First Page: Show

Primary Subjects: 60F10

Secondary Subjects: 60G99

Keywords: Weibull sojourn source; large deviation; nonlinear scale; nonconvex rate function

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jap/1208358955
Digital Object Identifier: doi:10.1239/jap/1208358955
Mathematical Reviews number (MathSciNet): MR2409314
Zentralblatt MATH identifier: 1137.60012

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Project Euclid: euclid.aop/1022855755

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Digital Object Identifier: doi:10.1214/aop/1176994938

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Zentralblatt MATH: 0418.60033

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