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Hawkes process with tempered Mittag-Leffler kernel

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  • Gupta, Neha
  • Maheshwari, Aditya

Abstract

In this paper, we propose an extension of the Hawkes process by incorporating a kernel based on the tempered Mittag–Leffler distribution. This is the generalization of the work presented in Habyarimana et al., (2023). blue This kernel unifies and extends both the exponential and Mittag-Leffler forms, enabling the modeling of processes with both short and long memory behavior. We derive analytical results for the expectation of the conditional intensity and the expected number of events in the counting process. In addition, we investigate the limiting behavior of the expectation of the conditional intensity. Finally, we present an empirical comparison of the studied process with its limiting special cases.

Suggested Citation

  • Gupta, Neha & Maheshwari, Aditya, 2026. "Hawkes process with tempered Mittag-Leffler kernel," Statistics & Probability Letters, Elsevier, vol. 234(C).
    • Handle: RePEc:eee:stapro:v:234:y:2026:i:c:s0167715226000258
    DOI: 10.1016/j.spl.2026.110661
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