# Multiscale Piecewise Deterministic Markov Process in infinite dimension: central limit theorem and Langevin approximation

ESAIM: Probability and Statistics (2014)

- Volume: 18, page 541-569
- ISSN: 1292-8100

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topGenadot, A., and Thieullen, M.. "Multiscale Piecewise Deterministic Markov Process in infinite dimension: central limit theorem and Langevin approximation." ESAIM: Probability and Statistics 18 (2014): 541-569. <http://eudml.org/doc/274343>.

@article{Genadot2014,

abstract = {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.},

author = {Genadot, A., Thieullen, M.},

journal = {ESAIM: Probability and Statistics},

keywords = {piecewise deterministic Markov process; averaging principle; neuron model},

language = {eng},

pages = {541-569},

publisher = {EDP-Sciences},

title = {Multiscale Piecewise Deterministic Markov Process in infinite dimension: central limit theorem and Langevin approximation},

url = {http://eudml.org/doc/274343},

volume = {18},

year = {2014},

}

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

PB - EDP-Sciences

VL - 18

SP - 541

EP - 569

AB - 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.

LA - eng

KW - piecewise deterministic Markov process; averaging principle; neuron model

UR - http://eudml.org/doc/274343

ER -

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