6 citations · 12 across the 4 of their papers we have counts for
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Ergodicity and limit theorems for degenerate diffusions with time periodic drift. Applications to a stochastic Hodgkin-Huxley model
R. Höpfner, E. Löcherbach, M. Thieullen
We formulate simple criteria for positive Harris recurrence of strongly degenerate stochastic differential equations with smooth coefficients when the drift depends on time and spa…
Strongly degenerate time inhomogeneous SDEs: densities and support properties. Application to a Hodgkin-Huxley system with periodic input
Reinhard Höpfner, E. Löcherbach, M. Thieullen
In this paper we study the existence of densities for strongly degenerate stochastic differential equations (SDEs) whose coefficients depend on time and are not globally Lipschitz.…
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…
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…