Institut für Mathematik | AG Stochastik | Statistik stochastischer Prozesse


Neurons and stochastic processes

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Unpublished note 2010, arxiv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

Last Update: February 2, 2023
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