Process-level large deviations for nonlinear Hawkes point processes
Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 3, pp. 845-871.

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.

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.

DOI : 10.1214/12-AIHP532
Classification : 60G55, 60F10
Mots-clés : large deviations, rare events, point processes, Hawkes processes, self-exciting processes 
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Zhu, Lingjiong. Process-level large deviations for nonlinear Hawkes point processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 3, pp. 845-871. doi : 10.1214/12-AIHP532. http://archive.numdam.org/articles/10.1214/12-AIHP532/

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