| Full text | |
| Author(s): |
Total Authors: 4
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| Affiliation: | [1] Univ Cergy Pontoise, AGM UMR CNRS 8088, 2 Ave Adolphe Chauvin, F-95302 Cergy Pontoise - France
[2] Univ Sao Paulo, Sao Paulo - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Stochastic Processes and their Applications; v. 129, n. 1, p. 1-27, JAN 2019. |
| Web of Science Citations: | 2 |
| Abstract | |
We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in R d and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the evolution of a typical neuron, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis. (C) 2018 Elsevier B.V. All rights reserved. (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 |
| FAPESP's process: | 16/17791-9 - Interacting processes with variable range memory in neurobiological models |
| Grantee: | Aline Duarte de Oliveira |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 16/17789-4 - Stability, statistical selection of models and hydrodynamic boundary for interacting chains with variable reach memory |
| Grantee: | Guilherme Ost de Aguiar |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |