Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data, The European Physical Journal B, vol.96, issue.5, pp.1-12, 2012. ,
DOI : 10.1140/epjb/e2012-21005-8
URL : https://hal.archives-ouvertes.fr/hal-01313844
Scaling limits for Hawkes processes and application to financial statistics, 2012. ,
Modeling and predicting popularity dynamics of microblogs using self-excited Hawkes processes. arXiv preprint, 2015. ,
Refractoriness and neural precision, Journal of Neuroscience, vol.18, issue.6, pp.2200-2211, 1998. ,
Connecting Mean Field Models of Neural Activity to EEG and fMRI Data, Brain Topography, vol.157, issue.60, pp.139-149, 2010. ,
DOI : 10.1007/s10548-010-0140-3
Point processes and queues, 1981. ,
DOI : 10.1007/978-1-4684-9477-8
Stability of nonlinear Hawkes processes, Ann. Probab, vol.24, issue.3, pp.1563-1588, 1996. ,
Weak-Strong Uniqueness for Measure-Valued Solutions, Communications in Mathematical Physics, vol.50, issue.12, p.351, 2011. ,
DOI : 10.1007/s00220-011-1267-0
URL : http://arxiv.org/abs/0912.1028
Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates, Neural Computation, vol.15, issue.7, pp.1621-1671, 1999. ,
DOI : 10.1038/373612a0
Measure Solutions for Some Models in Population Dynamics, Acta Applicandae Mathematicae, vol.48, issue.3, pp.141-156, 2013. ,
DOI : 10.1007/s10440-012-9758-3
Microscopic approach of a time elapsed neural model, Mathematical Models and Methods in Applied Sciences, vol.25, issue.14, pp.252669-2719, 2015. ,
DOI : 10.1142/S021820251550058X
URL : https://hal.archives-ouvertes.fr/hal-01159215
Detection of dependence patterns with delay, Biometrical Journal, vol.26, issue.6, pp.1110-1130, 2015. ,
DOI : 10.1002/bimj.201400235
URL : https://hal.archives-ouvertes.fr/hal-00998864
Maximum likelihood identification of neural point process systems, Biological Cybernetics, vol.80, issue.4-5, pp.265-275, 1988. ,
DOI : 10.1080/01621459.1985.10477119
Robust dynamic classes revealed by measuring the response function of a social system, Proceedings of the National Academy of Sciences, pp.15649-15653, 2008. ,
DOI : 10.1073/pnas.0803685105
Global solvability of a networked integrate-and-fire model of McKean???Vlasov type, The Annals of Applied Probability, vol.25, issue.4, pp.2096-2133, 2015. ,
DOI : 10.1214/14-AAP1044
URL : https://hal.archives-ouvertes.fr/hal-00747565
Particle systems with a singular mean-field self-excitation. Application to neuronal networks, Stochastic Processes and their Applications, pp.2451-2492, 2015. ,
DOI : 10.1016/j.spa.2015.01.007
URL : https://hal.archives-ouvertes.fr/hal-01001716
Hawkes processes on large networks, The Annals of Applied Probability, vol.26, issue.1, pp.216-261, 2016. ,
DOI : 10.1214/14-AAP1089
URL : https://hal.archives-ouvertes.fr/hal-01102806
Oscillations and concentrations in weak solutions of the incompressible fluid equations, Communications in Mathematical Physics, vol.38, issue.4, pp.667-689, 1987. ,
DOI : 10.1007/BF01214424
Asymptotic description of stochastic neural networks. I. Existence of a large deviation principle, Comptes Rendus Mathematique, vol.352, issue.10, pp.841-846, 2014. ,
DOI : 10.1016/j.crma.2014.08.018
URL : https://hal.archives-ouvertes.fr/hal-01074827
A constructive mean-field analysis of multi population neural networks with random synaptic weights and stochastic inputs, Frontiers in Computational Neuroscience, vol.3, 2009. ,
DOI : 10.3389/neuro.10.001.2009
URL : https://hal.archives-ouvertes.fr/inria-00258345
On the rate of convergence in Wasserstein distance of the empirical measure. Probability Theory and Related Fields, pp.1-32, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00915365
On a toy model of interacting neurons. arXiv preprint, 2014. ,
Interpretation of the Repetitive Firing of Nerve Cells, The Journal of General Physiology, vol.45, issue.6, pp.1163-1179, 1962. ,
DOI : 10.1085/jgp.45.6.1163
Modeling networks of spiking neurons as interacting processes with memory of variable length, 2015. ,
Spiking neuron models: Single neurons, populations, plasticity, 2002. ,
DOI : 10.1017/CBO9780511815706
Statistical models based on counting processes, 1997. ,
FADO: A Statistical Method to Detect Favored or Avoided Distances between Occurrences of Motifs using the Hawkes' Model, Statistical Applications in Genetics and Molecular Biology, vol.4, issue.1, 2005. ,
DOI : 10.2202/1544-6115.1119
Lasso and probabilistic inequalities for multivariate point processes, Bernoulli, vol.21, issue.1, pp.83-143, 2015. ,
DOI : 10.3150/13-BEJ562
URL : https://hal.archives-ouvertes.fr/hal-00722668
Spectra of some self-exciting and mutually exciting point processes, Biometrika, vol.58, issue.1, pp.83-90, 1971. ,
DOI : 10.1093/biomet/58.1.83
A cluster process representation of a self-exciting process, Journal of Applied Probability, pp.493-503, 1974. ,
Abstract, Advances in Applied Probability, vol.22, issue.01, 2014. ,
DOI : 10.1017/S0143385700000924
Statistical distributions of earthquake numbers: consequence of branching process, Geophysical Journal International, vol.180, issue.3, pp.1313-1328, 2010. ,
DOI : 10.1111/j.1365-246X.2009.04487.x
Probability theory: a comprehensive course, 2007. ,
Simulation of nonhomogeneous poisson processes by thinning, Naval Research Logistics Quarterly, vol.32, issue.3, pp.403-413, 1979. ,
DOI : 10.1002/nav.3800260304
Multivariate Hawkes processes, 2009. ,
Mean field limit for disordered diffusions with singular interactions, The Annals of Applied Probability, vol.24, issue.5, pp.1946-1993, 2014. ,
DOI : 10.1214/13-AAP968
Stability results for a general class of interacting point processes dynamics, and applications. Stochastic processes and their applications, pp.1-30, 1998. ,
Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models, Probabilistic models for nonlinear partial differential equations (Montecatini Terme, pp.42-95, 1995. ,
DOI : 10.1007/BF01055714
Self-Exciting Point Process Modeling of Crime, Journal of the American Statistical Association, vol.106, issue.493, p.106, 2011. ,
DOI : 10.1198/jasa.2011.ap09546
On Lewis' simulation method for point processes, IEEE Transactions on Information Theory, vol.27, issue.1, pp.23-30, 1981. ,
DOI : 10.1109/TIT.1981.1056305
Space-Time Point-Process Models for Earthquake Occurrences, Annals of the Institute of Statistical Mathematics, vol.50, issue.2, pp.379-402, 1998. ,
DOI : 10.1023/A:1003403601725
Dynamics of a structured neuron population, Nonlinearity, vol.23, issue.1, p.55, 2010. ,
DOI : 10.1088/0951-7715/23/1/003
URL : https://hal.archives-ouvertes.fr/hal-00387413
Relaxation and Self-Sustained Oscillations in the Time Elapsed Neuron Network Model, SIAM Journal on Applied Mathematics, vol.73, issue.3, pp.1260-1279, 2013. ,
DOI : 10.1137/110847962
Adaptation and Fatigue Model for Neuron Networks and Large Time Asymptotics in a Nonlinear Fragmentation Equation, The Journal of Mathematical Neuroscience, vol.4, issue.1, pp.1-26, 2014. ,
DOI : 10.1016/j.jmaa.2005.12.036
URL : https://hal.archives-ouvertes.fr/hal-01054561
Transport equations in biology, 2006. ,
Automatic spike train analysis and report generation. An implementation with R, R2HTML and STAR, Journal of Neuroscience Methods, vol.181, issue.1, pp.119-144, 2009. ,
DOI : 10.1016/j.jneumeth.2009.01.037
URL : https://hal.archives-ouvertes.fr/hal-00725386
A microscopic spiking neuronal network for the age-structured model. arXiv preprint, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01121061
Goodness-of-Fit Tests and Nonparametric Adaptive Estimation for Spike Train Analysis, The Journal of Mathematical Neuroscience, vol.4, issue.1, pp.1-41, 2014. ,
DOI : 10.1109/TIT.1981.1056305
URL : https://hal.archives-ouvertes.fr/hal-01100718
Adaptive estimation for Hawkes processes; application to genome analysis. The Annals of Statistics, pp.2781-2822, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00863958
Time-frequency analysis of locally stationary Hawkes processes. prepublication on HAL, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01502252
Topics in propagation of chaos, Lecture Notes in Math, vol.22, issue.1, pp.165-251, 1991. ,
DOI : 10.1070/SM1974v022n01ABEH001689
Gaussian approximation of nonlinear Hawkes processes, The Annals of Applied Probability, vol.26, issue.4, pp.2106-2140 ,
DOI : 10.1214/15-AAP1141
Poisson approximation of point processes with stochastic intensity, and application to nonlinear Hawkes processes, Ann. Inst. H. Poincaré Probab. Statist ,
Central Limit Theorem for Nonlinear Hawkes Processes, Journal of Applied Probability, vol.I, issue.03, pp.760-771, 2013. ,
DOI : 10.1214/aop/1065725193
URL : http://arxiv.org/abs/1204.1067
Nonlinear Hawkes Processes, 2013. ,
Process-level large deviations for nonlinear Hawkes point processes, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.50, issue.3, pp.845-871, 2014. ,
DOI : 10.1214/12-AIHP532
URL : http://arxiv.org/abs/1108.2431
Large deviations for Markovian nonlinear Hawkes processes, The Annals of Applied Probability, vol.25, issue.2, pp.548-581 ,
DOI : 10.1214/14-AAP1003