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Limit theorems for discrete Hawkes processes

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  • Seol, Youngsoo

Abstract

We consider discrete time Hawkes process which is a class of g-functions. The limit theorems for continuous time Hawkes processes are well known and studied by many authors. In this paper, we study the limit theorems for discrete time Hawkes processes. In particular, we obtain the law of large number, the central limit theorem and the invariance principle.

Suggested Citation

  • Seol, Youngsoo, 2015. "Limit theorems for discrete Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 223-229.
    • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:223-229
    DOI: 10.1016/j.spl.2015.01.023
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    References listed on IDEAS

    as
    1. Behzad Mehrdad & Lingjiong Zhu, 2014. "On the Hawkes Process with Different Exciting Functions," Papers 1403.0994, arXiv.org, revised Sep 2017.
    2. Zhu, Lingjiong, 2013. "Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 544-550.
    3. Zhu, Lingjiong, 2013. "Moderate deviations for Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 885-890.
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    Citations

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    Cited by:

    1. Huang, Lorick & Khabou, Mahmoud, 2023. "Nonlinear Poisson autoregression and nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 201-241.
    2. Seol, Youngsoo, 2017. "Limit theorems for the compensator of Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 165-172.
    3. Seol, Youngsoo, 2019. "Limit theorems for an inverse Markovian Hawkes process," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    4. Wang, Haixu, 2022. "Limit theorems for a discrete-time marked Hawkes process," Statistics & Probability Letters, Elsevier, vol. 184(C).
    5. Kim, Gunhee & Choe, Geon Ho, 2019. "Limit properties of continuous self-exciting processes," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    6. Youngsoo Seol, 2023. "Large Deviations for Hawkes Processes with Randomized Baseline Intensity," Mathematics, MDPI, vol. 11(8), pages 1-10, April.
    7. Youngsoo Seol, 2022. "Non-Markovian Inverse Hawkes Processes," Mathematics, MDPI, vol. 10(9), pages 1-12, April.

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