Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Process-level large deviations for nonlinear Hawkes point processes

Lingjiong Zhu

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Abstract

In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit formula.

Résumé

Dans cet article nous prouvons un principe de grandes déviations de niveau trois pour une classe très générale de processus ponctuels, c’est à dire les processus de Hawkes non-linéaires ; nous obtenons une formule explicite pour la fonctionnelle de taux, donnée par l’entropie au niveau du processus.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 50, Number 3 (2014), 845-871.

Dates
First available in Project Euclid: 20 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1403277000

Digital Object Identifier
doi:10.1214/12-AIHP532

Mathematical Reviews number (MathSciNet)
MR3224291

Zentralblatt MATH identifier
1296.60129

Subjects
Primary: 60G55: Point processes 60F10: Large deviations

Keywords
Large deviations Rare events Point processes Hawkes processes Self-exciting processes

Citation

Zhu, Lingjiong. Process-level large deviations for nonlinear Hawkes point processes. Ann. Inst. H. Poincaré Probab. Statist. 50 (2014), no. 3, 845--871. doi:10.1214/12-AIHP532. https://projecteuclid.org/euclid.aihp/1403277000


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References

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