تقرير
On a finite-size neuronal population equation
| العنوان: | On a finite-size neuronal population equation |
|---|---|
| المؤلفون: | Schmutz, Valentin, Löcherbach, Eva, Schwalger, Tilo |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, 60G55 (primary) 60H20, 60K35, 92B20 (secondary) |
| الوصف: | 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 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2106.14721 |
| رقم الأكسشن: | edsarx.2106.14721 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |