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

Khashayar Pakdaman, Michèle Thieullen and Gilles Wainrib

Stochastic Processes and their Applications, 2012, vol. 122, issue 6, 2292-2318

Abstract: 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.

Keywords: Piecewise-deterministic Markov process; Averaging; Homogenization; Central limit theorem; Multiscale; Slow-fast; Neuron models with stochastic ion channels (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:6:p:2292-2318

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DOI: 10.1016/j.spa.2012.03.005

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