24 citations · 63 across the 20 of their papers we have counts for
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math.PR2011★ 4 cited
Limit theorems for infinite-dimensional piecewise deterministic Markov processes. Applications to stochastic excitable membrane models
Martin G. Riedler, Michèle Thieullen, Gilles Wainrib
We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous…
math.PR2011★ 6 cited
Averaging for a Fully-Coupled Piecewise Deterministic Markov Process in Infinite Dimension
Alexandre Genadot, Michèle Thieullen
In this paper, we consider the generalized Hodgkin-Huxley model introduced by Austin in \cite{Austin}. This model describes the propagation of an action potential along the axon of…