Article Dans Une Revue Stochastic Processes and their Applications Année : 2022

MULTIVARIATE HAWKES PROCESSES ON INHOMOGENEOUS RANDOM GRAPHS

Résumé

We consider a population of $N$ interacting neurons, represented by a multivariate Hawkes process: the firing rate of each neuron depends on the history of the connected neurons. Contrary to the mean-field framework where the interaction occurs on the complete graph, the connectivity between particles is given by a random possibly diluted and inhomogeneous graph where the probability of presence of each edge depends on the spatial position of its vertices. We address the well-posedness of this system and Law of Large Numbers results as $N\to\infty$. A crucial issue will be to understand how spatial inhomogeneity influences the large time behavior of the system.

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Dates et versions

hal-03264303 , version 1 (22-06-2021)
hal-03264303 , version 2 (22-02-2022)

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Zoé Agathe-Nerine. MULTIVARIATE HAWKES PROCESSES ON INHOMOGENEOUS RANDOM GRAPHS. Stochastic Processes and their Applications, 2022, 152, pp.86-148. ⟨10.1016/j.spa.2022.06.019⟩. ⟨hal-03264303v2⟩
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