Institut
für Mathematik | AG
Stochastik | Statistik stochastischer Prozesse| Institut
für Mathematik | AG
Stochastik | Statistik stochastischer Prozesse |
|
R. Höpfner and K. Brodda, A stochastic model and a functional limit
theorem for information processing in large systems of neurons.
Journal of Mathematical Biology 52(4), 439-457 (2006),
pdf
R. Höpfner, On a set of data for the membrane potential in a neuron.
Math. Biosciences 207(2), 275-301 (2007),
pdf
R. Höpfner, To which extent is the membrane potential in a neuron
between successive spikes adequately modelled by a (continuous) semimartingale?
Unpublished note 2010, arxiv
R. Höpfner, E. Löcherbach, M. Thieullen, Ergodicity for a
stochastic Hodgkin-Huxley model driven by Ornstein-Uhlenbeck type input.
Ann. Inst. H. Poincaré 52(1), 483-501 (2016), arxiv
R. Höpfner, E. Löcherbach, M. Thieullen, Strongly degenerate
time inhomogeneous SDEs: densities and support properties. Application
to Hodgkin-Huxley type systems.
Bernoulli 23(4A), 2587-2616 (2017), pdf
R. Höpfner, E. Löcherbach, M. Thieullen, Ergodicity and limit
theorems for degenerate diffusions with time periodic drift. Applications
to a stochastic Hodgkin-Huxley model.
ESAIM P+S 20, 527-554 (2016), arxiv
R. Höpfner, Polynomials under
Ornstein-Uhlenbeck noise and an application to inference in stochastic
Hodgkin-Huxley systems.
Statistical Inference Stoch. Processes 24, 35--59 (2021), pdf
R. Hoepfner, 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. Mathematical Neuroscience and Applications 3, 1--38 (2023)
arXiv: 2203.16160
R. Hoepfner, R code associated to
the paper arXiv:2203:16160v1 submitted to MNA
| Institut
für Mathematik | AG
Stochastik | Statistik stochastischer Prozesse |
