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Pré-Publication, Document De Travail Année : 2023

LONG-TERM STABILITY OF INTERACTING HAWKES PROCESSES ON RANDOM GRAPHS

Zoé Agathe-Nerine
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Résumé

We consider a population of Hawkes processes modeling the activity of $N$ interacting neurons. The neurons are regularly positioned on the segment $[0,1]$, and the connectivity between neurons 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 through a spatial kernel. The main result of the paper concerns the long-time stability of the synaptic current of the population, as $N\to\infty$, in the subcritical regime in case the synaptic memory kernel is exponential, up to time horizons that are polynomial in $N$.
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Dates et versions

hal-03739494 , version 1 (27-07-2022)
hal-03739494 , version 2 (11-07-2023)

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Zoé Agathe-Nerine. LONG-TERM STABILITY OF INTERACTING HAWKES PROCESSES ON RANDOM GRAPHS. 2023. ⟨hal-03739494v2⟩
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