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Limit theorems for a discrete-time marked Hawkes process

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  • Wang, Haixu

Abstract

Hawkes process is a self-exciting point process with wide applications in many fields, such as finance, seismology, and ecology. Hawkes processes are defined for the continuous-time setting. However, data is often recorded in a discrete-time or aggregated scheme. To model the temporal process in aggregated way, oftentimes a discrete-time type Hawkes process is more desirable. In this paper, we study the limit theorems for a discrete-time marked Hawkes process first proposed in Xu et al. (2020).

Suggested Citation

  • Wang, Haixu, 2022. "Limit theorems for a discrete-time marked Hawkes process," Statistics & Probability Letters, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:stapro:v:184:y:2022:i:c:s0167715222000037
    DOI: 10.1016/j.spl.2022.109368
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    References listed on IDEAS

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    1. Thibault Jaisson & Mathieu Rosenbaum, 2013. "Limit theorems for nearly unstable Hawkes processes," Papers 1310.2033, arXiv.org, revised Mar 2015.
    2. Seol, Youngsoo, 2015. "Limit theorems for discrete Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 223-229.
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    4. Luc, BAUWENS & Nikolaus, HAUTSCH, 2006. "Modelling Financial High Frequency Data Using Point Processes," Discussion Papers (ECON - Département des Sciences Economiques) 2006039, Université catholique de Louvain, Département des Sciences Economiques.
    5. 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.
    6. Horst, Ulrich & Xu, Wei, 2021. "Functional limit theorems for marked Hawkes point measures," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 94-131.
    7. 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.
    8. Zailei Cheng & Youngsoo Seol, 2020. "Diffusion Approximation of a Risk Model with Non-Stationary Hawkes Arrivals of Claims," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 555-571, June.
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    Cited by:

    1. Youngsoo Seol, 2023. "Large Deviations for Hawkes Processes with Randomized Baseline Intensity," Mathematics, MDPI, vol. 11(8), pages 1-10, April.

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