Multivariate Hawkes processes on inhomogeneous random graphs

Zoé Agathe-Nerine

Stochastic Processes and their Applications, 2022, vol. 152, issue C, 86-148

Abstract: 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→∞. A crucial issue will be to understand how spatial inhomogeneity influences the large time behavior of the system.

Keywords: Multivariate nonlinear Hawkes processes; Mean-field systems; Neural networks; Spatially extended system; Random graph; Graph convergence (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.06.019

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