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

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  • Pakdaman, Khashayar
  • Thieullen, Michèle
  • Wainrib, Gilles

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.

Suggested Citation

  • Pakdaman, Khashayar & Thieullen, Michèle & Wainrib, Gilles, 2012. "Asymptotic expansion and central limit theorem for multiscale piecewise-deterministic Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2292-2318.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:6:p:2292-2318
    DOI: 10.1016/j.spa.2012.03.005
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    References listed on IDEAS

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    1. Bryc, Wlodzimierz, 1993. "A remark on the connection between the large deviation principle and the central limit theorem," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 253-256, November.
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