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Moderate deviations for Hawkes processes

Author

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  • Zhu, Lingjiong

Abstract

In this paper, we obtain a moderate deviation principle for a class of point processes, i.e. linear Hawkes processes.

Suggested Citation

  • Zhu, Lingjiong, 2013. "Moderate deviations for Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 885-890.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:3:p:885-890
    DOI: 10.1016/j.spl.2012.12.011
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    References listed on IDEAS

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    1. V. Chavez-Demoulin & A. C. Davison & A. J. McNeil, 2005. "Estimating value-at-risk: a point process approach," Quantitative Finance, Taylor & Francis Journals, vol. 5(2), pages 227-234.
    2. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    3. Chen, Xia, 2001. "Moderate deviations for Markovian occupation times," Stochastic Processes and their Applications, Elsevier, vol. 94(1), pages 51-70, July.
    4. Luc Bauwens & Nikolaus Hautsch, 2009. "Modelling Financial High Frequency Data Using Point Processes," Springer Books, in: Thomas Mikosch & Jens-Peter Kreiß & Richard A. Davis & Torben Gustav Andersen (ed.), Handbook of Financial Time Series, chapter 41, pages 953-979, Springer.
    5. Large, Jeremy, 2007. "Measuring the resiliency of an electronic limit order book," Journal of Financial Markets, Elsevier, vol. 10(1), pages 1-25, February.
    6. Gao, Fu-Qing, 1996. "Moderate deviations for martingales and mixing random processes," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 263-275, February.
    7. Gusto Gaelle & Schbath Sophie, 2005. "FADO: A Statistical Method to Detect Favored or Avoided Distances between Occurrences of Motifs using the Hawkes' Model," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-28, September.
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    Citations

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    Cited by:

    1. Seol, Youngsoo, 2015. "Limit theorems for discrete Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 223-229.
    2. Seol, Youngsoo, 2017. "Limit theorems for the compensator of Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 165-172.
    3. Youngsoo Seol, 2023. "Large Deviations for Hawkes Processes with Randomized Baseline Intensity," Mathematics, MDPI, vol. 11(8), pages 1-10, April.
    4. Kim, Gunhee & Choe, Geon Ho, 2019. "Limit properties of continuous self-exciting processes," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    5. Lingjiong Zhu, 2015. "A State-Dependent Dual Risk Model," Papers 1510.03920, arXiv.org, revised Feb 2023.
    6. Seol, Youngsoo, 2019. "Limit theorems for an inverse Markovian Hawkes process," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    7. Gao, Fuqing & Zhu, Lingjiong, 2018. "Some asymptotic results for nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4051-4077.
    8. Sarma, Utpal Jyoti Deba & Selvamuthu, Dharmaraja, 2024. "Study of discrete-time Hawkes process and its compensator," Statistics & Probability Letters, Elsevier, vol. 214(C).
    9. Behzad Mehrdad & Lingjiong Zhu, 2014. "On the Hawkes Process with Different Exciting Functions," Papers 1403.0994, arXiv.org, revised Sep 2017.
    10. 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).
    11. 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.
    12. 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.
    13. Youngsoo Seol, 2022. "Non-Markovian Inverse Hawkes Processes," Mathematics, MDPI, vol. 10(9), pages 1-12, April.

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