Multiscale Piecewise Deterministic Markov Process in infinite dimension: central limit theorem and Langevin approximation∗. (10th October 2014)

• Record Type: Journal Article
• Authors: Genadot, A.; Thieullen, M.
• Is Part Of: ESAIM. Volume 18(2014)
• Page Start: 541
• Page End: 569
• Publication Date: 2014-10-10
• Subjects: Piecewise deterministic Markov process, -- averaging principle, -- neuron model; Probabilities -- Periodicals; Mathematical statistics -- Periodicals; 519.2
• DOI: 10.1051/ps/2013051
• Languages: English
• ISSNs: 1292-8100

Abstract

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.