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December 2015 Large deviations for multidimensional state-dependent shot-noise processes
Amarjit Budhiraja, Pierre Nyquist
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J. Appl. Probab. 52(4): 1097-1114 (December 2015). DOI: 10.1239/jap/1450802755

Abstract

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.

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Amarjit Budhiraja. Pierre Nyquist. "Large deviations for multidimensional state-dependent shot-noise processes." J. Appl. Probab. 52 (4) 1097 - 1114, December 2015. https://doi.org/10.1239/jap/1450802755

Information

Published: December 2015
First available in Project Euclid: 22 December 2015

zbMATH: 1334.60028
MathSciNet: MR3439174
Digital Object Identifier: 10.1239/jap/1450802755

Subjects:
Primary: 60F10, 60G55
Secondary: 60K30

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 4 • December 2015
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