  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.
