| Texto completo | |
| Autor(es): |
Loecherbach, E.
Número total de Autores: 1
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| 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 |