M. Ableidinger, A stochastic version of the Jansen and Rit neural mass model: Analysis and numerics', Journal of Mathematical Neuroscience, 2017.

V. Bally and &. Talay, The law of the Euler scheme for stochastic differential equations I. Convergence rate of the distribution function, Monte Carlo Methods and Applications, vol.2, pp.93-128, 1996.
URL : https://hal.archives-ouvertes.fr/inria-00074427

R. W. Berg and &. S. Ditlevsen, Synaptic inhibition and excitation estimated via the time constant of membrane potential fluctuations, J Neurophys, vol.110, pp.1021-1034, 2013.

P. Cattiaux, Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation. I. Invariant density'. Stochastic Processes and their, Applications, vol.124, pp.1236-1260, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01044611

P. Cattiaux, Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation, II. Drift term'. ALEA, vol.11, pp.359-384, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01044611

P. Cattiaux, Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation. III. Diffusion term, Annals of Applied Probability, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01044611

F. Comte, Adaptive estimation for stochastic damping Hamiltonian systems under partial observation'. Stochastic Processes and Their Applications To appear, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01659337

S. Coombes and &. Byrne, Lecture Notes in Nonlinear Dynamics in Computational Neuroscience: from Physics and Biology to ICT, chap. Next generation neural mass models, 2017.

P. Dayan and &. L. Abbott, Theoretical Neuroscience, 2001.

P. D. Moral, The Monte-Carlo method for filtering with discrete-time observations, Probab. Theory Related Fields, vol.120, issue.3, pp.346-368, 2001.

B. Delyon, Convergence of a stochastic approximation version of the EM algorithm, Ann. Statist, vol.27, pp.94-128, 1999.

A. Dempster, Maximum likelihood from incomplete data via the EM algorithm, Jr. R. Stat. Soc. B, vol.39, pp.1-38, 1977.

R. Deville, Two distinct mechanisms of coherence in randomly perturbed dynamical systems, Physical Review E, vol.72, 2005.

P. Ditlevsen, The fast climate fluctuations during the stadial and interstadial climate states, Annals of Glaciology, vol.35, pp.457-462, 2002.

S. Ditlevsen and &. Greenwood, The Morris-Lecar neuron model embeds a leaky integrate-and-fire model', Journal of Mathematical Biology, vol.67, issue.2, pp.239-259, 2013.

S. Ditlevsen and &. E. Löcherbach, Multi-class oscillating systems of interacting neurons, Stochastic Processes and Their Applications, vol.127, pp.1840-1869, 2017.

S. Ditlevsen and &. A. Samson, Estimation in the partially observed stochastic MorrisLecar neuronal model with particle filter and stochastic approximation methods, Annals of Applied Statistics, vol.2, pp.674-702, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00712331

S. Ditlevsen and &. Sørensen, Inference for observations of integrated diffusion processes'. Scand, J. Statist, vol.31, issue.3, pp.417-429, 2004.

A. Doucet, An introduction to sequential Monte Carlo methods'. In Sequential Monte Carlo methods in practice, Stat. Eng. Inf. Sci, pp.3-14, 2001.

R. Fitzhugh, Impulses and Physiological States in Theoretical Models of Nerve Membrane', Biophysical Journal, vol.1, issue.6, pp.445-466, 1961.

V. Genon-catalot and &. J. Jacod, On the estimation of the diffusion coefficient for multi-dimensional diffusion processes, Ann. Inst. H. Poincaré Probab. Statist, vol.29, issue.1, pp.119-151, 1993.

V. Genon-catalot, Stochastic volatility models as hidden Markov models and statistical applications, Bernoulli, vol.6, issue.6, pp.1051-1079, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00693752

A. Gloter, Parameter estimation for a discretely observed integrated diffusion process'. Scand, J. Statist, vol.33, issue.1, pp.83-104, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00404901

J. H. Goldwyn and &. E. Shea-brown, The What and Where of Adding Channel Noise to the Hodgkin-Huxley Equations, PLOS Computational Biology, vol.7, issue.11, 2011.

P. C. Hall-&-c and . Heyde, Martingale limit theory and its application, 1980.

A. Hodgkin and &. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve', Journal of Physiology-London, vol.117, issue.4, pp.500-544, 1952.

A. Jensen, A Markov Chain Monte Carlo approach to parameter estimation in the FitzHugh-Nagumo model, Physical Review E, vol.86, p.41114, 2012.

M. Kessler, Estimation of an ergodic diffusion from discrete observations', Scand. J. Statist, vol.24, issue.2, pp.211-229, 1997.

P. E. Kloeden and &. E. Platen, Numerical Solution of Stochastic Differential Equations, 1992.

A. L. Breton and &. M. Musiela, Some parameter estimation problems for hypoelliptic homogeneous Gaussian diffusions, Banach Center Publications, vol.16, issue.1, pp.337-356, 1985.

B. Leimkuhler and &. Matthews, Molecular Dynamics with deterministic and stochastic numerical methods, vol.39, 2015.

J. Leon and &. A. Samson, Hypoelliptic stochastic FitzHugh-Nagumo neuronal model: mixing, up-crossing and estimation of the spike rate, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01492590

J. Mattingly, Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise, Stochastic Process. Appl, vol.101, pp.185-232, 2002.

J. Nagumo, An active pulse transmission line simulating nerve axon, Proc. Inst. Radio Eng, vol.50, pp.2061-2070, 1962.

G. Pavliotis and &. A. Stuart, Multiscale Methods. Averaging and Homogenization, 2008.

Y. Pokern, Parameter estimation for partially observed hypoelliptic diffusions, J. Roy. Stat. Soc. B, vol.71, issue.1, pp.49-73, 2009.

A. Samson-&-m.-thieullen, Contrast estimator for completely or partially observed hypoelliptic diffusion, Stochastic Processes and Their Applications, vol.122, pp.2521-2552, 2012.

M. Sørensen, Statistical methods for stochastic differential equations, chap. Estimating functions for diffusion-type processes, Chapman & Hall/CRC Monographs on Statistics & Applied Probability, pp.1-107, 2012.

H. C. Tuckwell and &. S. Ditlevsen, The Space-Clamped Hodgkin-Huxley System with Random Synaptic Input: Inhibition of Spiking by Weak Noise and Analysis with Moment Equations', Neural Computation, vol.28, issue.10, pp.2129-2161, 2016.