Asymptotic expansion and central limit theorem for multiscale piecewise-deterministic Markov processes

We consider a general class of piecewise-deterministic Markov processes with multiple time-scales. In line with recent results on the stochastic averaging principle for these processes, we obtain a description of their law through an asymptotic expansion. We further study the fluctuations around the averaged system in the form of a central limit theorem, and derive consequences on the law of the first passage-time. We apply the mathematical results to the Morris-Lecar model with stochastic ion channels. (C) 2012 Elsevier B.V. All rights reserved.