Multiscale Piecewise Deterministic Markov Process in Infinite Dimension: Central Limit Theorem and Langevin Approximation

2012/11/08 by Genadot, A., Thieullen, M.
#35K57 #60B12 #60J75 #92C20 #92C45 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1211.1894

Abstract

In [20], the authors addressed the question of the averaging of a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimension. In the present paper, we carry on and complete this work by the mathematical analysis of the fluctuation of the slow-fast system around the averaged limit. A central limit theorem is derived and the associated Langevin approximation is considered. The motivation of this work is a stochastic Hodgkin-Huxley model which describes the propagation of an action potential along the nerve fiber. We study this PDMP in detail and provide more general results for a class of Hilbert space valued PDMP.

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