Diffusion approximation of multi-class Hawkes processes: theoretical and numerical analysis

Orateur: Anna MELNYKOVA
Localisation: Université Grenoble Alpes, France
Type: Séminaire de probabilités et statistiques
Site: UGE , 4B 125
Date de début: 02/03/2021 - 10:30
Date de fin: 02/03/2021 - 11:30

Oscillatory systems of interacting Hawkes processes with Erlang memory kernels were introduced in Ditlevsen & Loecherbach (2017). They are piecewise deterministic Markov processes (PDMP) and can be approximated by a stochastic diffusion. First, a strong error bound between the PDMP and the diffusion is proved. Second, moment bounds for the resulting diffusion are derived. Third, approximation schemes for the diffusion, based on the numerical splitting approach, are proposed. These schemes are proved to converge with mean-square order 1 and to preserve the properties of the diffusion, in particular the hypoellipticity, the ergodicity and the moment bounds. Finally, the PDMP and the diffusion are compared through numerical experiments, where the PDMP is simulated with an adapted thinning procedure.

Joint work with Julien Chevallier d'Université Grenoble Alpes and Irene Tubikanec de JKU Linz (Autriche).