Process-level large deviations for nonlinear Hawkes point processes

Lingjiong Zhu

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 3, page 845-871
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Zhu, Lingjiong. "Process-level large deviations for nonlinear Hawkes point processes." Annales de l'I.H.P. Probabilités et statistiques 50.3 (2014): 845-871. <http://eudml.org/doc/272067>.

@article{Zhu2014,
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.},
author = {Zhu, Lingjiong},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {large deviations; rare events; point processes; Hawkes processes; self-exciting processes},
language = {eng},
number = {3},
pages = {845-871},
publisher = {Gauthier-Villars},
title = {Process-level large deviations for nonlinear Hawkes point processes},
url = {http://eudml.org/doc/272067},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Zhu, Lingjiong
TI - Process-level large deviations for nonlinear Hawkes point processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 3
SP - 845
EP - 871
AB - 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.
LA - eng
KW - large deviations; rare events; point processes; Hawkes processes; self-exciting processes
UR - http://eudml.org/doc/272067
ER -

References

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  11. [11] G. Stabile and G. L. Torrisi. Risk processes with non-stationary Hawkes arrivals. Methodol. Comput. Appl. Probab.12 (2010) 415–429. Zbl1231.91239MR2665268
  12. [12] S. R. S. Varadhan. Special invited paper: Large deviations. Ann. Probab.36 (2008) 397–419. Zbl1146.60003
  13. [13] S. R. S. Varadhan. Large Deviations and Applications. SIAM, Philadelphia, 1984. Zbl0549.60023MR758258
  14. [14] L. Zhu. Large deviations for Markovian nonlinear Hawkes processes. Preprint, 2011. Available at arXiv:1108.2432. Zbl1312.60019MR3313748
  15. [15] L. Zhu. Central limit theorem for nonlinear Hawkes processes. J. Appl. Probab.50 (2013) 760–771. Zbl1306.60015MR3102513

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