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Mean-field limit of generalized Hawkes processes

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  • Chevallier, Julien

Abstract

We generalize multivariate Hawkes processes mainly by including a dependence with respect to the age of the process, i.e. the delay since the last point.

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  • Chevallier, Julien, 2017. "Mean-field limit of generalized Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3870-3912.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:12:p:3870-3912
    DOI: 10.1016/j.spa.2017.02.012
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    1. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
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    Cited by:

    1. Duval, Céline & Luçon, Eric & Pouzat, Christophe, 2022. "Interacting Hawkes processes with multiplicative inhibition," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 180-226.
    2. Cormier, Quentin & Tanré, Etienne & Veltz, Romain, 2020. "Long time behavior of a mean-field model of interacting neurons," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2553-2595.
    3. Heesen, Sophie & Stannat, Wilhelm, 2021. "Fluctuation limits for mean-field interacting nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 280-297.
    4. Gao, Xuefeng & Zhu, Lingjiong, 2018. "Limit theorems for Markovian Hawkes processes with a large initial intensity," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3807-3839.
    5. Chevallier, J. & Duarte, A. & Löcherbach, E. & Ost, G., 2019. "Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 1-27.
    6. Agathe-Nerine, Zoé, 2022. "Multivariate Hawkes processes on inhomogeneous random graphs," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 86-148.
    7. Antonov, A. & Leonidov, A. & Semenov, A., 2021. "Self-excited Ising game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    8. Xuefeng Gao & Lingjiong Zhu, 2018. "Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 161-206, October.
    9. Li, Bo & Pang, Guodong, 2022. "Functional limit theorems for nonstationary marked Hawkes processes in the high intensity regime," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 285-339.
    10. Gao, Fuqing & Zhu, Lingjiong, 2018. "Some asymptotic results for nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4051-4077.
    11. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2017. "Hybrid marked point processes: characterisation, existence and uniqueness," Papers 1707.06970, arXiv.org, revised Oct 2018.
    12. Schmutz, Valentin, 2022. "Mean-field limit of age and leaky memory dependent Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 39-59.
    13. Pfaffelhuber, P. & Rotter, S. & Stiefel, J., 2022. "Mean-field limits for non-linear Hawkes processes with excitation and inhibition," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 57-78.

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