24 citations · 63 across the 20 of their papers we have counts for
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math.PR2013★ 4 cited
Ergodicity for a stochastic Hodgkin-Huxley model driven by Ornstein-Uhlenbeck type input
R. Höpfner, E. Löcherbach, M. Thieullen
We consider a model describing a neuron and the input it receives from its dendritic tree when this input is a random perturbation of a periodic deterministic signal, driven by an…
math.PR2013★ 1 cited
Transition densities for strongly degenerate time inhomogeneous random models
R. Höpfner, E. Löcherbach, M. Thieullen
In this paper we study the existence of densities for strongly degenerate stochastic differential equations whose coefficients depend on time and are not globally Lipschitz. In the…
math.PR2013
Spatio-Temporal Hybrid (PDMP) Models: Central Limit Theorem and Langevin Approximation for Global Fluctuations. Application to Electrophysiology
Martin G Riedler, Michele Thieullen
In the present work we derive a Central Limit Theorem for sequences of Hilbert-valued Piecewise Deterministic Markov process models and their global fluctuations around their deter…