Large Deviations for Cascades of Diffusions Arising in Oscillating Systems of Interacting Hawkes Processes

Autor(es)

Loecherbach, E.

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF THEORETICAL PROBABILITY; v. 32, n. 1, p. 131-162, MAR 2019.
• Citações Web of Science: 1

Resumo

We consider oscillatory systems of interacting Hawkes processes introduced in Ditlevsen and Locherbach (Stoch Process Appl 2017, http://arxiv.org/abs/1512.00265) 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. (AU)

• Processo FAPESP: 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat
• Beneficiário: Oswaldo Baffa Filho
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs