Fluid limit theorems for stochastic hybrid systems with application to neuron models
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Publication:3059695
DOI10.1239/AAP/1282924062zbMATH Open1232.60019arXiv1001.2474OpenAlexW2963569544WikidataQ56907233 ScholiaQ56907233MaRDI QIDQ3059695
Author name not available (Why is that?)
Publication date: 26 November 2010
Published in: (Search for Journal in Brave)
Abstract: This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump Markov processes. We prove a functional law of large numbers with exponential convergence speed, derive a diffusion approximation and establish a functional central limit theorem. We apply these results to neuron models with stochastic ion channels, as the number of channels goes to infinity, estimating the convergence to the deterministic model. In terms of neural coding, we apply our central limit theorems to estimate numerically impact of channel noise both on frequency and spike timing coding.
Full work available at URL: https://arxiv.org/abs/1001.2474
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