Volume 18, 2014
|Page(s)||541 - 569|
|Published online||10 October 2014|
Multiscale Piecewise Deterministic Markov Process in infinite dimension: central limit theorem and Langevin approximation∗
Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie
Curie, Paris 6, Case courrier 188, 4 Place Jussieu, 75252 Paris Cedex 05, France
Revised: 19 June 2013
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.
Mathematics Subject Classification: 60B12 / 60J75 / 35K57
Key words: Piecewise deterministic Markov process / averaging principle / neuron model
© EDP Sciences, SMAI 2014
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