| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Cergy Pontoise, CNRS, UMR 8088, Dept Math, 2 Ave Adolphe Chauvin, F-95302 Cergy Pontoise - France
[2] Univ Rennes 1, CNRS UMR 6625, Inst Rech Math Rennes, Campus Beaulieu, Batiment 22, F-35042 Rennes - France
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES; v. 21, n. 1, p. 81-111, APR 2018. |
| Web of Science Citations: | 3 |
| Abstract | |
We consider a model of interacting neurons where the membrane potentials of the neurons are described by a multidimensional piecewise deterministic Markov process with values in R-N, where N is the number of neurons in the network. A deterministic drift attracts each neuron's membrane potential to an equilibrium potential m. When a neuron jumps, its membrane potential is reset to a resting potential, here 0, while the other neurons receive an additional amount of potential 1/N. We are interested in the estimation of the jump (or spiking) rate of a single neuron based on an observation of the membrane potentials of the N neurons up to time t. We study a Nadaraya-Watson type kernel estimator for the jump rate and establish its rate of convergence in L-2. This rate of convergence is shown to be optimal for a given Holder class of jump rate functions. We also obtain a central limit theorem for the error of estimation. The main probabilistic tools are the uniform ergodicity of the process and a fine study of the invariant measure of a single neuron. (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 |