Pseudo-chaotic expansion and explicit correlation formula for the Hawkes processes

18.10.2023, 12:00  –  Haus 9, Raum 2.22
Forschungsseminar Wahrscheinlichkeitstheorie

Anthony Réveillac (INSA Toulouse)

Hawkes processes have proved to be a powerful probabilistic model for various applications in neurosciences or insurance. These counting processes are defined through their intensity which is stochastic and pathwise dependent on the historical values of the process itself. This implicit definition leads to important drawbacks for performing explicit calculations involving simple quantities like for instance the inter-temporal correlation for which nothing is known to our knowledge outside the stationary case and some very particular examples. In this talk based on a joint work with C. Hillairet (ENSAE Paris), we will fill this gap by exploiting a specific decomposition named pseudo-chaotic expansion mixing some pathwise calculus together with some Malliavin calculus obtained in a previous joint work.

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