P. Abry, P. Gonçalvès, and P. Flandrin, Wavelets, spectrum analysis and 1/f processes, pp.1529978-1529979, 1995.
DOI : 10.1007/978-1-4612-2544-7_2
URL : https://hal.archives-ouvertes.fr/inria-00570663

W. Bair, C. Koch, W. Newsome, and K. Britten, Power spectrum analysis of bursting cells in area mt in the behaving monkey, Journal of Neuroscience, vol.1414, issue.55, p.28702892, 1994.

J. Beran, Y. Feng, S. Ghosh, and R. Kulik, Long-memory processes ISBN 978-3-642-35511-0, Probabilistic properties and statistical methods, pp.978-981, 2013.

J. Bhattacharya, J. Edwards, A. Mamelak, and E. Schuman, Long-range temporal correlations in the spontaneous spiking of neurons in the hippocampal-amygdala complex of humans, Neuroscience, vol.131, issue.2, p.547555, 2005.
DOI : 10.1016/j.neuroscience.2004.11.013

R. N. Bhattacharya, V. K. Gupta, and E. Waymire, The Hurst eect under trends, J. Appl. Probab, vol.20, issue.3, p.649662, 1983.
DOI : 10.1017/s0021900200023895

N. Brunel and S. Sergi, Firing frequency of leaky intergrate-and-re neurons with synaptic current dynamics, Journal of Theoretical Biology, vol.1958795, issue.1, 1998.

A. Cardinali and G. P. Nason, Costationarity of Locally Stationary Time Series, Journal of Time Series Econometrics, vol.2, issue.2, 1074.
DOI : 10.2202/1941-1928.1074
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.306.7181

A. Cardinali and G. P. Nason, Practical powerful wavelet packet tests for second-order stationarity Applied and Computational Harmonic Analysis
DOI : 10.1016/j.acha.2016.06.006

P. Carmona, L. Coutin, and G. Montseny, Approximation of some Gaussian processes

M. J. Chacron, K. Pakdaman, and A. Longtin, Interspike interval correlations, memory, adaptation, and refractoriness in a leaky integrate-and-re model with threshold fatigue, Neural Computation, vol.15, issue.2, p.253278, 2003.

A. M. Churilla, W. A. Gottschalke, L. S. Liebovitch, L. Y. Selector, A. T. Todorov et al., Membrane potential uctuations of human t-lymphocytes have fractal characteristics of fractional brownian motion, Annals of Biomedical Engineering, vol.24, issue.1, p.99108, 1995.

J. Coeurjolly, Simulation and identication of the fractional brownian motion: a bibliographical and comparative study, Journal of Statistical Software, vol.5153, issue.1, 2000.

L. Decreusefond and D. Nualart, Hitting times for Gaussian processes, The Annals of Probability, vol.36, issue.1, p.319330, 2008.
DOI : 10.1214/009117907000000132
URL : https://hal.archives-ouvertes.fr/hal-00079171

M. Delorme and K. J. Wiese, Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory, Physical Review Letters, vol.115, issue.21
DOI : 10.1103/PhysRevLett.115.210601

A. Destexhe, M. Rudolph, and D. Paré, The high-conductance state of neocortical neurons in vivo, Nat Rev Neurosci, vol.4, issue.9, p.739751, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00299172

P. J. Drew and L. F. Abbott, Models and Properties of Power-Law Adaptation in Neural Systems, Journal of Neurophysiology, vol.96, issue.2, p.826833826, 2006.
DOI : 10.1152/jn.00134.2006

N. Enriquez, A simple construction of the fractional Brownian motion, Stochastic Processes and their Applications, vol.109, issue.2, p.203223, 2004.
DOI : 10.1016/j.spa.2003.10.008
URL : https://hal.archives-ouvertes.fr/hal-00101987

G. L. 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

A. Hammond and S. Sheeld, Power law P??lya???s urn and fractional Brownian motion, Probability Theory and Related Fields, vol.5, issue.3
DOI : 10.1007/s00440-012-0468-6
URL : http://arxiv.org/abs/0903.1284

. Probab, Theory Related Fields, pp.440-452

A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, vol.117, issue.4, p.500544, 1952.
DOI : 10.1113/jphysiol.1952.sp004764

B. S. Jackson, Including long-range dependence in integrate-and-re models of the high interspike-interval variability of cortical neurons, Neural Computation, issue.10, p.16

D. Kwiatkowski, P. C. Phillips, P. Schmidt, and Y. Shin, Testing the null hypothesis of stationarity against the alternative of a unit root, Journal of Econometrics, vol.54, issue.1-3, pp.159-178, 1992.
DOI : 10.1016/0304-4076(92)90104-Y

C. D. Lewis, G. L. Gebber, P. D. Larsen, and S. M. Barman, Long-term correlations in the spike trains of medullary sympathetic neurons, Journal of Neurophysiology, vol.8585, issue.44, pp.1614-1622, 1614.

B. Lindner, Interspike interval statistics of neurons driven by colored noise, Physical Review E, vol.69, issue.2, p.22901, 2004.
DOI : 10.1103/PhysRevE.69.022901

S. B. Lowen, S. S. Cash, M. Poo, and M. C. Teich, Quantal neurotransmitter secretion rate exhibits fractal behavior, Journal of Neuroscience, vol.17, issue.15, p.56665677, 1997.
DOI : 10.1007/978-1-4757-9800-5_3

S. B. Lowen, T. Ozaki, E. Kaplan, B. E. Saleh, and M. C. Teich, Fractal Features of Dark, Maintained, and Driven Neural Discharges in the Cat Visual System, Methods, vol.24, issue.4, pp.377-394, 2001.
DOI : 10.1006/meth.2001.1207

B. N. Lundstrom, M. H. Higgs, W. J. Spain, and A. L. , Fractional dierentiation by neocortical pyramidal neurons, Nat Neurosci, vol.11, issue.11, p.13351342, 2008.
DOI : 10.1038/nn.2212
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2596753

B. B. Mandelbrot, Limit theorems on the self-normalized range for weakly and strongly dependent processes, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.31, issue.4, p.271285, 1974.
DOI : 10.1007/BF00532867

B. B. Mandelbrot-la-loi-climatologique and H. E. Hurst, Une classe de processus stochastiques homothétiques à soi, C. R. Acad. Sci. Paris, vol.260, p.32743277, 1965.

R. Metzler and J. Klafter, The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics, Journal of Physics A: Mathematical and General, vol.37, issue.31, pp.161-2080305, 2004.
DOI : 10.1088/0305-4470/37/31/R01

J. W. Middleton, M. J. Chacron, B. Lindner, and A. Longtin, Firing statistics of a neuron model driven by long-range correlated noise, Physical Review E, vol.68, issue.2, p.21920, 2003.
DOI : 10.1103/PhysRevE.68.021920

G. Nason, A test for second-order stationarity and approximate condence intervals for localized autocovariances for locally stationary time series, J. R. Stat. Soc. Ser. B. Stat. Methodol, vol.75, issue.5

. Stanley, Long-range correlations in nucleotide sequences, Nature, vol.356, p.168170, 1992.

C. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley et al., Mosaic organization of DNA nucleotides, Physical Review E, vol.49, issue.2, p.16851689, 1994.
DOI : 10.1103/PhysRevE.49.1685

M. B. Priestley, T. Subba, and . Rao, A test for non-stationarity of time-series, 1<140:ATFNOT>2.0.CO;2-V&origin=MSN, pp.140149-140184, 1969.

G. Rangarajan and M. Ding, Processes with long-range correlations: Theory and applications, Lecture Notes in Physics, vol.621, 2003.
DOI : 10.1007/3-540-44832-2

D. Revuz and M. Yor, Continuous martingales and Brownian motion, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1999.

A. Richard and D. Talay, Hölder continuity in the Hurst parameter of functionals of Stochastic Dierential Equations driven by fractional Brownian motion, 2016.

L. Sacerdote and M. T. Giraudo, Stochastic integrate and re models: a review on mathematical methods and their applications, Stochastic biomathematical models, pp.99148978-99148981

G. Samorodnitsky, Stochastic processes and long range dependence Springer Series in Operations Research and Financial Engineering ISBN 978-3-319- 45574-7, pp.978-981, 2016.
DOI : 10.1007/978-3-319-45575-4

T. Schwalger and L. Schimansky-geier, Interspike interval statistics of a leaky integrate-and-fire neuron driven by Gaussian noise with large correlation times, Physical Review E, vol.77, issue.3, p.31914, 2008.
DOI : 10.1103/PhysRevE.77.031914

T. Schwalger, K. Fisch, J. Benda, and B. Lindner, How Noisy Adaptation of Neurons Shapes Interspike Interval Histograms and Correlations, PLoS Computational Biology, vol.81, issue.12, 2010.
DOI : 10.1371/journal.pcbi.1001026.g014
URL : http://doi.org/10.1371/journal.pcbi.1001026

T. Schwalger, F. Droste, and B. Lindner, Statistical structure of neural spiking under non-Poissonian or other non-white stimulation, Journal of Computational Neuroscience, vol.89, issue.6
DOI : 10.1007/s10827-015-0560-x

R. Segev, M. Benveniste, E. Hulata, N. Cohen, A. Palevski et al., Long term behavior of lithographically prepared in vitro neuronal networks

C. Sobie, A. Babul, and R. De-sousa, noise, Physical Review E, vol.83, issue.5, p.51912, 2011.
DOI : 10.1103/PhysRevE.83.051912

T. Sottinen, Fractional Brownian motion, random walks and binary market models, Finance and Stochastics, vol.5, issue.3, p.343355, 2001.
DOI : 10.1007/PL00013536
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.74.8084

M. S. Taqqu, Weak convergence to fractional Brownian motion and to the Rosenblatt process, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, vol.31, p.287302, 1974.
DOI : 10.2307/1426060

M. S. Taqqu, V. Teverovsky, and W. Willinger, ESTIMATORS FOR LONG-RANGE DEPENDENCE: AN EMPIRICAL STUDY, Fractals, vol.03, issue.04, p.3785798, 1995.
DOI : 10.1142/S0218348X95000692

M. C. Teich, Fractal neuronal ring patterns, Single Neuron Computation, Neural Networks: Foundations to Applications, pp.589-625, 1992.

M. C. Teich, R. G. Turcott, and R. M. Siegel, Temporal correlation in cat striate-cortex neural spike trains, IEEE Engineering in Medicine and Biology Magazine, vol.15, issue.5, pp.7987-7997, 1996.
DOI : 10.1109/51.537063

M. C. Teich, C. Heneghan, S. B. Lowen, T. Ozaki, and E. Kaplan, Fractal character of the neural spike train in the visual system of the cat, Journal of the Optical Society of America A, vol.14, issue.3, p.529546, 1997.
DOI : 10.1364/JOSAA.14.000529

R. Weron, Estimating long-range dependence: nite sample properties and condence intervals, Phys. A, vol.312, issue.1202, pp.285299-0378, 2002.
DOI : 10.1016/s0378-4371(02)00961-5
URL : http://arxiv.org/abs/cond-mat/0103510

W. Willinger, M. S. Taqqu, R. Sherman, and D. V. Wilson, Self-similarity through highvariability: Statistical analysis of ethernet lan trac at the source level, IEEE/ACM Trans. Netw, vol.5, issue.1, p.7186