  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.
