Large deviations for multidimensional state-dependent shot-noise processes

A. Budhiraja, P. Nyquist

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)

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 stateindependent 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.

Original languageEnglish
Pages (from-to)1097-1114
Number of pages18
JournalJournal of Applied Probability
Volume52
Issue number4
DOIs
Publication statusPublished - 1 Dec 2015
Externally publishedYes

Keywords

  • Large deviations
  • Poisson random measure
  • Poisson shot-noise
  • Variational representations

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