Large deviations for cascades of diffusions arising in oscillating systems of interacting Hawkes processes
Probability
2017-09-28 v1
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 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.
Keywords
Cite
@article{arxiv.1709.09356,
title = {Large deviations for cascades of diffusions arising in oscillating systems of interacting Hawkes processes},
author = {Eva Löcherbach},
journal= {arXiv preprint arXiv:1709.09356},
year = {2017}
}