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math.PR2012★ 1 cited
Multiscale Piecewise Deterministic Markov Process in Infinite Dimension: Central Limit Theorem and Langevin Approximation
A. Genadot, M. Thieullen
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 a…
math.PR2012
Transition densities for stochastic Hodgkin-Huxley models
Reinhard Höpfner, Eva Löcherbach, Michèle Thieullen
We consider a stochastic Hodgkin-Huxley model driven by a periodic signal as model for the membrane potential of a pyramidal neuron. The associated five dimensional diffusion proce…