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The Large Deviation Principle for the On-Off Weibull Sojourn Process

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Ken R. Duffy  and
Artem Sapozhnikov
Ken R. Duffy*
Affiliation:
National University of Ireland, Maynooth
Artem Sapozhnikov*
Affiliation:
Centrum voor Wiskunde en Informatica
*
∗Postal address: Hamilton Institute, National University of Ireland, Maynooth, Co. Kildare, Ireland.
∗∗Postal address: Centrum voor Wiskunde en Informatica, Kruislaan 413, NL-1098SJ Amsterdam, Holland.
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Abstract

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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.

Keywords

Weibull sojourn sourcelarge deviationnonlinear scalenonconvex rate function

MSC classification

Secondary: 60F10: Large deviations 60G99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 1 , March 2008 , pp. 107 - 117
Copyright
Copyright © Applied Probability Trust 2008 

References

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