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This paper establishes limit theorems for a class of stochastic hybridsystems (continuous deterministic dynamic coupled with jump Markov processes)in the fluid limit (small jumps at high frequency), thus extending knownresults for jump Markov processes. We prove a functional law of large numberswith exponential convergence speed, derive a diffusion approximation andestablish a functional central limit theorem. We apply these results to neuronmodels with stochastic ion channels, as the number of channels goes toinfinity, estimating the convergence to the deterministic model. In terms ofneural coding, we apply our central limit theorems to estimate numericallyimpact of channel noise both on frequency and spike timing coding.

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