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

M. Thieullen (1) , K. Pakdaman , G. Wainrib

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Domaines: Probabilités [math.PR]

M. Thieullen, K. Pakdaman, G. Wainrib. Asymptotic expansion and central limit theorem for multiscale piecewise-deterministic Markov processes. Stochastic Processes and their Applications, 2012, 122 (6), pp.2292-2318. ⟨10.1016/j.spa.2012.03.005⟩. ⟨hal-00714354⟩