Fluid limit theorems for stochastic hybrid systems with application to neuron models

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.
Document type :
Preprints, Working Papers, ...
42 pages, 4 figures. 2010
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00447808
Contributor : Michele Thieullen <>
Submitted on : Friday, January 15, 2010 - 7:37:17 PM
Last modification on : Wednesday, October 12, 2016 - 1:03:01 AM

Identifiers

  • HAL Id : hal-00447808, version 1
  • ARXIV : 1001.2474

Collections

INSMI | PMA | UPMC | USPC

Citation

K. Pakdaman, M. Thieullen, G. Wainrib. Fluid limit theorems for stochastic hybrid systems with application to neuron models. 42 pages, 4 figures. 2010. 〈hal-00447808〉

Share

Metrics

Consultations de la notice

86