MULTIVARIATE HAWKES PROCESSES ON INHOMOGENEOUS RANDOM GRAPHS - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2021

MULTIVARIATE HAWKES PROCESSES ON INHOMOGENEOUS RANDOM GRAPHS

Zoé Agathe-Nerine
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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 graphs 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 the behaviour as $N\to\infty$. A crucial issue will be to understand how spatial inhomogeneity influences the large time behaviour 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. 2021. ⟨hal-03264303v1⟩
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