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Limit Theorems for an extended inverse Hawkes process with general exciting functions

Author

Listed:
  • Selvamuthu, Dharmaraja
  • Pandey, Shamiksha
  • Tardelli, Paola

Abstract

An inverse Hawkes process is a process having constant intensity and stochastic jump size, depending on the past number of jumps, while a Hawkes process has the intensity which is stochastic. An extended inverse Hawkes process is a process obtained by combining a Hawkes process and an inverse Hawkes process.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:197:y:2023:i:c:s016771522300041x
    DOI: 10.1016/j.spl.2023.109817
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    References listed on IDEAS

    as
    1. Gao, Fuqing & Zhu, Lingjiong, 2018. "Some asymptotic results for nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4051-4077.
    2. Seol, Youngsoo, 2017. "Limit theorems for the compensator of Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 165-172.
    3. Zhu, Lingjiong, 2013. "Moderate deviations for Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 885-890.
    4. 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.
    5. Seol, Youngsoo, 2019. "Limit theorems for an inverse Markovian Hawkes process," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    6. Youngsoo Seol, 2022. "Non-Markovian Inverse Hawkes Processes," Mathematics, MDPI, vol. 10(9), pages 1-12, April.
    Full references (including those not matched with items on IDEAS)

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