Ergodicity for a stochastic Hodgkin-Huxley model driven by Ornstein-Uhlenbeck type input

DOI10.1214/14-AIHP647zbMath1335.60091arXiv1311.3458OpenAlexW2963132702MaRDI QIDQ5963226

Reinhard Hoepfner, Eva Löcherbach, Michèle Thieullen

Publication date: 4 March 2016

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.3458

zbMATH Keywords

degenerate diffusion processesdendritic treeperiodic ergodicityspiking neuronstochastic Hodgkin-Huxley modeltime-inhomogeneous diffusion processesweak Hörmander condition

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Neural biology (92C20) Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (12)

Tube estimates for diffusion processes under a weak Hörmander condition ⋮ On a stochastic neuronal model integrating correlated inputs ⋮ \(Q\)-processes and asymptotic properties of Markov processes conditioned not to hit moving boundaries ⋮ Spectral Theory for Random Poincaré Maps ⋮ Ergodicity and limit theorems for degenerate diffusions with time periodic drift. Application to a stochastic Hodgkin−Huxley model ⋮ An ergodic theorem for asymptotically periodic time-inhomogeneous Markov processes, with application to quasi-stationarity with moving boundaries ⋮ Positive Harris recurrence for degenerate diffusions with internal variables and randomly perturbed time-periodic input ⋮ Parametric inference for hypoelliptic ergodic diffusions with full observations ⋮ Local asymptotic normality for shape and periodicity of a signal in the drift of a degenerate diffusion with internal variables ⋮ Exact pathwise simulation of multi-dimensional Ornstein-Uhlenbeck processes ⋮ Polynomials under Ornstein-Uhlenbeck noise and an application to inference in stochastic Hodgkin-Huxley systems ⋮ From random Poincaré maps to stochastic mixed-mode-oscillation patterns

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