In [A. Genadot and M. Thieullen, Averaging for a fully coupled piecewise-deterministic markov process in infinite dimensions. Adv. Appl. Probab. 44 (2012) 749-773], the authors addressed the question of averaging for a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimensions. In the present paper, we carry on and complete this work by the mathematical analysis of the fluctuations of the slow-fast system around the averaged limit. A central limit theorem is derived and the associated Langevin approximation is considered. The motivation for this work is the study of stochastic conductance based neuron models which describe the propagation of an action potential along a nerve fiber.
Mots-clés : piecewise deterministic Markov process, averaging principle, neuron model
@article{PS_2014__18__541_0,
author = {Genadot, A. and Thieullen, M.},
title = {Multiscale {Piecewise} {Deterministic} {Markov} {Process} in infinite dimension: central limit theorem and {Langevin} approximation},
journal = {ESAIM: Probability and Statistics},
pages = {541--569},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2013051},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2013051/}
}
TY - JOUR AU - Genadot, A. AU - Thieullen, M. TI - Multiscale Piecewise Deterministic Markov Process in infinite dimension: central limit theorem and Langevin approximation JO - ESAIM: Probability and Statistics PY - 2014 SP - 541 EP - 569 VL - 18 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2013051/ DO - 10.1051/ps/2013051 LA - en ID - PS_2014__18__541_0 ER -
%0 Journal Article %A Genadot, A. %A Thieullen, M. %T Multiscale Piecewise Deterministic Markov Process in infinite dimension: central limit theorem and Langevin approximation %J ESAIM: Probability and Statistics %D 2014 %P 541-569 %V 18 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2013051/ %R 10.1051/ps/2013051 %G en %F PS_2014__18__541_0
Genadot, A.; Thieullen, M. Multiscale Piecewise Deterministic Markov Process in infinite dimension: central limit theorem and Langevin approximation. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 541-569. doi : 10.1051/ps/2013051. http://archive.numdam.org/articles/10.1051/ps/2013051/
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