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| Full text | |
| Author(s): |
Loecherbach, E.
Total Authors: 1
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| Document type: | Journal article |
| Source: | JOURNAL OF THEORETICAL PROBABILITY; v. 32, n. 1, p. 131-162, MAR 2019. |
| Web of Science Citations: | 1 |
| Abstract | |
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) | |
| FAPESP's process: | 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat |
| Grantee: | Oswaldo Baffa Filho |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |