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A fractional Hawkes process II: further characterization of the process
journal contribution
posted on 2023-06-10, 06:17 authored by Cassien Habyarimana, Jane A Aduda, Enrico Scalas, Jing Chen, Alan G Hawkes, Federico PolitoWe characterize a Hawkes point process with kernel proportional to the probability density function of Mittag-Leffler random variables. This kernel decays as a power law with exponent $\beta +1 \in (1,2]$. Several analytical results can be proved, in particular for the expected intensity of the point process and for the expected number of events of the counting process. These analytical results are used to validate algorithms that numerically invert the Laplace transform of the expected intensity as well as Monte Carlo simulations of the process. Finally, Monte Carlo simulations are used to derive the full distribution of the number of events. The algorithms used for this paper are available at {\tt https://github.com/habyarimanacassien/Fractional-Hawkes}.
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- Published
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- Published version
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Physica A: Statistical Mechanics and its ApplicationsISSN
0378-4371Publisher
ElsevierExternal DOI
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615Page range
1-11Department affiliated with
- Mathematics Publications
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- Yes
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- Yes
Legacy Posted Date
2023-02-21First Open Access (FOA) Date
2023-02-23First Compliant Deposit (FCD) Date
2023-02-20Usage metrics
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