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

@article{Pakdaman2010FluidLT,
  title={Fluid limit theorems for stochastic hybrid systems with application to neuron models},
  author={Khashayar Pakdaman and Mich{\`e}le Thieullen and Gilles Wainrib},
  journal={Advances in Applied Probability},
  year={2010},
  volume={42},
  pages={761 - 794}
}
In this paper we establish limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamics 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… Expand
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