M. Bachar, J. Batzel, and S. Ditlevsen, Stochastic Biomathematical Models with Applications to Neuronal Modeling, 2013.

R. Berg, A. Alaburda, and J. Hounsgaard, Balanced Inhibition and Excitation Drive Spike Activity in Spinal Half-Centers, Science, vol.315, issue.5810, pp.315-390, 2007.
DOI : 10.1126/science.1134960

R. W. Berg and S. Ditlevsen, Synaptic inhibition and excitation estimated via the time constant of membrane potential fluctuations, Journal of Neurophysiology, vol.110, issue.4, pp.1021-1034, 2013.
DOI : 10.1152/jn.00006.2013

E. Bibbona and S. Ditlevsen, Estimation in Discretely Observed Diffusions Killed at a Threshold, Scandinavian Journal of Statistics, vol.73, issue.2, pp.274-293, 2013.
DOI : 10.1093/biomet/73.3.573

E. Bibbona, P. Lansky, and R. Sirovich, Estimating input parameters from intracellular recordings in the Feller neuronal model, Physical Review E, vol.2, issue.3, p.31916, 2010.
DOI : 10.1080/03610919908813596

A. Burkitt, A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input, Biological Cybernetics, vol.68, issue.1, pp.1-19, 2006.
DOI : 10.1007/978-3-642-93059-1

O. Cappé, E. Moulines, and T. And-ryden, Inference in Hidden Markov Models, 2005.

A. Destexhe, M. Rudolph, J. Fellous, and T. Sejnowski, Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons, Neuroscience, vol.107, issue.1, pp.13-24, 2001.
DOI : 10.1016/S0306-4522(01)00344-X

URL : https://hal.archives-ouvertes.fr/hal-00124691

A. Destexhe, M. Badoual, Z. Piwkowska, T. Bal, R. et al., A novel method for characterizing synaptic noise in cortical neurons, Neurocomputing, vol.58, issue.60, pp.58-60, 2004.
DOI : 10.1016/j.neucom.2004.01.042

URL : https://hal.archives-ouvertes.fr/hal-00018646

S. Ditlevsen and A. Samson, Stochastic Biomathematical Models with Applications to Neuronal Modeling, chapter Introduction to Stochastic Models in Biology, 2013.

S. Ditlevsen and A. Samson, Estimation in the partially observed stochastic Morris???Lecar neuronal model with particle filter and stochastic approximation methods, The Annals of Applied Statistics, vol.8, issue.2, pp.674-702, 2014.
DOI : 10.1214/14-AOAS729

URL : https://hal.archives-ouvertes.fr/hal-00712331

J. L. Forman and M. Sørensen, The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes, Scandinavian Journal of Statistics, vol.1, issue.3, pp.438-465, 2008.
DOI : 10.21314/JCF.2001.089

G. Gerstein and B. Mandelbrot, Random Walk Models for the Spike Activity of a Single Neuron, Biophysical Journal, vol.4, issue.1, pp.41-68, 1964.
DOI : 10.1016/S0006-3495(64)86768-0

W. Gerstner and W. Kistler, Spiking Neuron Models, 2002.

W. Gerstner, W. M. Kistler, R. Naud, and L. Paninski, Neuronal Dynamics . From single neurons to networks and models of cognition, 2014.

M. Habib and A. Thavaneswaran, Inference for stochastic neuronal models, Applied Mathematics and Computation, vol.38, issue.1, pp.51-73, 1990.
DOI : 10.1016/0096-3003(90)90080-M

A. Hodgkin and A. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, vol.117, issue.4, pp.500-544, 1952.
DOI : 10.1113/jphysiol.1952.sp004764

R. Hoepfner, On a set of data for the membrane potential in a neuron, Mathematical Biosciences, vol.207, issue.2, pp.275-301, 2007.
DOI : 10.1016/j.mbs.2006.10.009

Q. J. Huys and L. Paninski, Smoothing of, and Parameter Estimation from, Noisy Biophysical Recordings, PLoS Computational Biology, vol.87, issue.60, 2009.
DOI : 10.1371/journal.pcbi.1000379.s001

Q. J. Huys, M. Ahrens, and L. Paninski, Efficient Estimation of Detailed Single-Neuron Models, Journal of Neurophysiology, vol.96, issue.2, pp.872-890, 2006.
DOI : 10.1152/jn.00079.2006

S. M. Iacus, Simulation and Inference for Stochastic Differential Equations with R examples, 2008.

E. M. Izhikevich, Dynamical Systems in Neuroscience, 2007.

P. Jahn, R. W. Berg, J. Hounsgaard, and S. Ditlevsen, Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process, Journal of Computational Neuroscience, vol.21, issue.11, pp.563-579, 2011.
DOI : 10.1162/neco.2009.06-08-807

A. C. Jensen, S. Ditlevsen, M. Kessler, P. , and O. , Markov chain Monte Carlo approach to parameter estimation in the FitzHugh-Nagumo model, Physical Review E, vol.117, issue.4, p.41114, 2012.
DOI : 10.1016/j.spa.2012.04.006

P. Kloeden and E. Platen, Numerical solution of stochastic differential equations, 1992.

M. Kostuk, B. A. Toth, C. D. Meliza, D. Margoliash, and H. D. Abarbanel, Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods, Biological Cybernetics, vol.105, issue.3, pp.155-167, 2012.
DOI : 10.1007/s00422-011-0459-1

C. Laing and G. J. Lord, Stochastic Methods in Neuroscience, 2010.
DOI : 10.1093/acprof:oso/9780199235070.001.0001

V. Lanska and P. Lansky, Input parameters in a one-dimensional neuronal model with reversal potentials, Biosystems, vol.48, issue.1-3, pp.123-129, 1998.
DOI : 10.1016/S0303-2647(98)00078-1

P. Lansky, Inference for the diffusion models of neuronal activity, Mathematical Biosciences, vol.67, issue.2, pp.247-260, 1983.
DOI : 10.1016/0025-5564(83)90103-7

P. Lansky, P. Sanda, and J. He, The parameters of the stochastic leaky integrate-and-fire neuronal model, Journal of Computational Neuroscience, vol.21, issue.2, pp.211-223, 2006.
DOI : 10.1007/s10827-006-8527-6

B. Øksendal, Stochastic Differential Equations: An Introduction with Applications, 2010.

L. Paninski, J. Pillow, and E. Simoncelli, Comparing integrate-and-fire models estimated using intracellular and extracellular data, Neurocomputing, vol.65, issue.66, pp.379-385, 2005.
DOI : 10.1016/j.neucom.2004.10.032

L. Paninski, Y. Ahmadian, D. G. Ferreira, S. Koyama, K. R. Rad et al., A new look at state-space models for neural data, Iss. SI), pp.107-126, 2010.
DOI : 10.1137/1.9781611970128

L. Paninski, M. Vidne, B. Depasquale, and D. G. Ferreira, Inferring synaptic inputs given a noisy voltage trace via sequential Monte Carlo methods, Journal of Computational Neuroscience, vol.27, issue.35, pp.1-19, 2012.
DOI : 10.1523/JNEUROSCI.2865-07.2007

O. Papaspiliopoulos, G. Roberts, and O. Stramer, Data Augmentation for Diffusions, Journal of Computational and Graphical Statistics, vol.85, issue.3, pp.665-688, 2013.
DOI : 10.1093/biomet/85.1.240

U. Picchini, S. Ditlevsen, D. Gaetano, A. Lansky, and P. , Parameters of the Diffusion Leaky Integrate-and-Fire Neuronal Model for a Slowly Fluctuating Signal, Neural Computation, vol.75, issue.2, pp.20-2696, 2008.
DOI : 10.1523/JNEUROSCI.4897-03.2004

M. Pospischil, Z. Piwkowska, M. Rudolph, T. Bal, and A. Destexhe, Calculating Event-Triggered Average Synaptic Conductances From the Membrane Potential, Journal of Neurophysiology, vol.97, issue.3, pp.2544-2552, 2007.
DOI : 10.1152/jn.01000.2006

URL : https://hal.archives-ouvertes.fr/hal-00120638

M. Pospischil, Z. Piwkowska, T. Bal, and A. Destexhe, Characterizing neuronal activity by describing the membrane potential as a stochastic process, Journal of Physiology-Paris, vol.103, issue.1-2, pp.98-106, 2009.
DOI : 10.1016/j.jphysparis.2009.05.010

URL : https://hal.archives-ouvertes.fr/hal-00444900

M. Pospischil, Z. Piwkowska, T. Bal, and A. Destexhe, Extracting synaptic conductances from single membrane potential traces, Neuroscience, vol.158, issue.2, pp.545-52, 2009.
DOI : 10.1016/j.neuroscience.2008.10.033

URL : https://hal.archives-ouvertes.fr/hal-00377094

P. Rao and B. , Statistical inference for diffusion type processes, 1999.

G. Roberts and O. Stramer, On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm, Biometrika, vol.88, issue.3, pp.603-621, 2001.
DOI : 10.1093/biomet/88.3.603

M. Rudolph and A. Destexhe, Characterization of Subthreshold Voltage Fluctuations in Neuronal Membranes, Neural Computation, vol.85, issue.11, pp.2577-2618, 2003.
DOI : 10.1006/jcph.1996.5638

URL : https://hal.archives-ouvertes.fr/hal-00123773

M. Rudolph, Z. Piwkowska, M. Badoual, T. Bal, and A. Destexhe, A Method to Estimate Synaptic Conductances From Membrane Potential Fluctuations, Journal of Neurophysiology, vol.91, issue.6, pp.91-2884, 2004.
DOI : 10.1152/jn.01223.2003

URL : https://hal.archives-ouvertes.fr/hal-00018654

M. Rudolph, J. Pelletier, D. Pare, and A. Destexhe, Estimation of synaptic conductances and their variances from intracellular recordings of neocortical neurons in vivo, Neurocomputing, vol.58, issue.60, pp.387-392, 2004.
DOI : 10.1016/j.neucom.2004.01.071

URL : https://hal.archives-ouvertes.fr/hal-00018652

A. Samson and M. Thieullen, A contrast estimator for completely or partially observed hypoelliptic diffusion, Stochastic Processes and their Applications, pp.2521-2552, 2012.
DOI : 10.1016/j.spa.2012.04.006

URL : https://hal.archives-ouvertes.fr/hal-00714352

H. Sørensen, Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey, International Statistical Review, vol.3, issue.3, pp.337-354, 2004.
DOI : 10.1017/S0266466600012044

M. Sørensen, Statistical Methods for Stochastic Differential Equations, chapter Estimating functions for diffusion type processes, 2012.

H. Tuckwell, Introduction to theoretical neurobiology Nonlinear and stochastic theories, 1988.