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Large deviations for multidimensional state-dependent shot noise processes
University of North Carolina at Chapel Hill United States.
Brown University, United States.ORCID iD: 0000-0001-8702-2293
2015 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 52, no 4, 1097-1114 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Applied Probability Trust , 2015. Vol. 52, no 4, 1097-1114 p.
Keyword [en]
Large deviations, point processes, Poisson random measure, shot noise
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-196797ISI: 000368467600013Scopus ID: 2-s2.0-84952888288OAI: oai:DiVA.org:kth-196797DiVA: diva2:1048753
Note

QC 20161122

Available from: 2016-11-22 Created: 2016-11-22 Last updated: 2016-11-22Bibliographically approved

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