3 papers
math.PR2022
On the long time behaviour of single stochastic Hodgkin-Huxley neurons with constant signal, and a construction of circuits of interacting neurons showing self-organized rhythmic oscillations
Reinhard Höpfner
The stochastic Hodgkin-Huxley neurons considered in this paper replace time-constant deterministic input of the classical deterministic model by increments $\vartheta dt + d…
math.PR2019
Ergodic branching diffusions with immigration: properties of invariant occupation measure, identification of particles under high-frequency observation, and estimation of the diffusion coefficient at nonparametric rates
Matthias Hammer, Reinhard Höpfner, Tobias Berg
In branching diffusions with immigration (BDI), particles travel on independent diffusion paths in , branch at position-dependent rates and leave offspring -- randoml…
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…