Hypoelliptic stochastic Fitzhugh-Nagumo neuronal model: mixing, up-crossing and estimation of the spike rate

DOI10.1214/17-AAP1355zbMath1406.92087OpenAlexW2615417224MaRDI QIDQ1617125

Adeline Samson, José Rafael León

Publication date: 7 November 2018

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aoap/1533780272

zbMATH Keywords

nonparametric estimationFitzhugh-Nagumo modelinvariant densityhypoelliptic diffusionpulse ratespike rate estimationup-crossings

Mathematics Subject Classification ID

Applications of statistics to biology and medical sciences; meta analysis (62P10) Nonparametric estimation (62G05) Neural biology (92C20) Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60)

Related Items (10)

A splitting method for SDEs with locally Lipschitz drift: illustration on the FitzHugh-Nagumo model ⋮ Estimation of distribution algorithms for the computation of innovation estimators of diffusion processes ⋮ High Order Splitting Methods for SDEs Satisfying a Commutativity Condition ⋮ Ergodicity and spike rate for stochastic FitzHugh-Nagumo neural model with periodic forcing ⋮ Consistency of a likelihood estimator for stochastic damping Hamiltonian systems. Totally observed data ⋮ Parametric inference for hypoelliptic ergodic diffusions with full observations ⋮ Adaptive estimation for degenerate diffusion processes ⋮ Density estimates and short-time asymptotics for a hypoelliptic diffusion process ⋮ Rate of estimation for the stationary distribution of stochastic damping Hamiltonian systems with continuous observations ⋮ Optimal control for parameter estimation in partially observed hypoelliptic stochastic differential equations

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