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Large deviations for multidimensional state-dependent shot-noise processes

Part of: Stochastic processes Special processes Limit theorems

Published online by Cambridge University Press:  30 March 2016

Amarjit Budhiraja  and
Pierre Nyquist
Amarjit Budhiraja*
Affiliation:
University of North Carolina at Chapel Hill
Pierre Nyquist*
Affiliation:
Brown University
*
∗Postal address: Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599, USA. Email address: [email protected]
∗∗Postal address: Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. Email address: [email protected]
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Abstract

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Shot-noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory, and in the engineering sciences. In this paper we prove a large deviation principle for the sample-paths of a general class of multidimensional state-dependent Poisson shot-noise processes. The result covers previously known large deviation results for one-dimensional state-independent shot-noise processes with light tails. We use the weak convergence approach to large deviations, which reduces the proof to establishing the appropriate convergence of certain controlled versions of the original processes together with relevant results on existence and uniqueness.

Keywords

Large deviationsPoisson shot-noisePoisson random measurevariational representations

MSC classification

Primary: 60F10: Large deviations 60G55: Point processes
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 4 , December 2015 , pp. 1097 - 1114
Copyright
Copyright © Applied Probability Trust 2015 

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