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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
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304414912000385
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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 6 ()
    Pages: 2292-2318

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:6:p:2292-2318

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    Related research

    Keywords: Piecewise-deterministic Markov process; Averaging; Homogenization; Central limit theorem; Multiscale; Slow-fast; Neuron models with stochastic ion channels;

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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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