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Some asymptotic results for nonlinear Hawkes processes

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  • Gao, Fuqing
  • Zhu, Lingjiong

Abstract

Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this paper, we study fluctuations, large deviations and moderate deviations nonlinear Hawkes processes in a new asymptotic regime, the large intensity function and the small exciting function regime. It corresponds to the large baseline intensity asymptotics for the linear case, and can also be interpreted as the asymptotics for the mean process of Hawkes processes on a large network.

Suggested Citation

  • Gao, Fuqing & Zhu, Lingjiong, 2018. "Some asymptotic results for nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4051-4077.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:12:p:4051-4077
    DOI: 10.1016/j.spa.2018.01.007
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    References listed on IDEAS

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    Cited by:

    1. Selvamuthu, Dharmaraja & Pandey, Shamiksha & Tardelli, Paola, 2023. "Limit Theorems for an extended inverse Hawkes process with general exciting functions," Statistics & Probability Letters, Elsevier, vol. 197(C).
    2. Seol, Youngsoo, 2019. "Limit theorems for an inverse Markovian Hawkes process," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    3. 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.
    4. Youngsoo Seol, 2023. "Large Deviations for Hawkes Processes with Randomized Baseline Intensity," Mathematics, MDPI, vol. 11(8), pages 1-10, April.
    5. Youngsoo Seol, 2022. "Non-Markovian Inverse Hawkes Processes," Mathematics, MDPI, vol. 10(9), pages 1-12, April.

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