Large deviations for cascades of diffusions arising in oscillating systems of interacting Hawkes processes

Eva Löcherbach

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arXiv · 1709.09356

Large deviations for cascades of diffusions arising in oscillating systems of interacting Hawkes processes

Eva Löcherbach

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Abstract

We consider oscillatory systems of interacting Hawkes processes introduced in Ditlevsen and Loecherbach (2017) to model multi-class systems of interacting neurons together with the diffusion approximations of their intensity processes. This diffusion, which incorporates the memory terms defining the dynamics of the Hawkes process, is hypo-elliptic. It is given by a high dimensional chain of differential equations driven by $2-$dimensional Brownian motion. We study the large-population-, i.e., small noise-limit of its invariant measure for which we establish a large deviation result in the spirit of Freidlin and Wentzell.

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Eva Löcherbach. 2017-09-27. Large deviations for cascades of diffusions arising in oscillating systems of interacting Hawkes processes. https://arxiv.org/abs/1709.09356

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