On a finite-size neuronal population equation
| Autor: | Schmutz, Valentin, Löcherbach, Eva, Schwalger, Tilo |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Population equations for infinitely large networks of spiking neurons have a long tradition in theoretical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear stochastic integral equation. We prove that, in the case of leaky integrate-and-fire (LIF) neurons with escape noise and for a slightly simplified version of the model, the equation is well-posed and stable in the sense of Br\'emaud-Massouli\'e. The proof combines methods from Markov processes taking values in the space of positive measures and nonlinear Hawkes processes. For applications, we also provide efficient simulation algorithms. Comment: 36 pages, 1 figure |
| Databáze: | arXiv |
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