Research
Area of research
- Temporal point processes : Hawkes processes, Poisson processes, discrete binary process.
- Interacting particle systems : propagation of chaos, law of large numbers, central limit theorem, spatial dependence.
- Simulation : temporal point processes, diffusion processes, joint simulation via KMT coupling.
- Transport equations : age structured equations, measure valued solutions.
- Mean field systems.
- Tests : independence test, multiple testing.
- Estimation : edge probability in a mean-field graph.
- Modelling : Large neural networks, oscillating systems.
- Data analysis : Detection of synchronous activity, coïncidence pattern, Unitary Events method, inference of the connectivity parameter.
Publications -- CV HAL
- Chevallier J., Caceres M. J., Doumic M., Reynaud-Bouret P. :
Microscopic approach of a time elapsed neural model ,
Mathematical Models and Methods in Applied Sciences, 25 (14), 2669-2719 (2015).
DOI : 10.1142/S021820251550058X.
- Chevallier J., Laloë T. :
Detection of dependence patterns with delay ,
Biometrical Journal, 57 (6), 1110-1130 (2015).
DOI : 10.1002/bimj.201400235.
- Chevallier J. :
Mean-field limit of generalized Hawkes processes ,
Stochastic Processes and their Applications, 127 (12), 3870-3912 (2017).
DOI : 10.1016/j.spa.2017.02.012.
- Chevallier J. :
Fluctuations for mean-field interacting age-dependent Hawkes processes ,
Electronic Journal of Probability, 22 (2017).
DOI : 10.1214/17-EJP63.
- Chevallier J. :
Stimulus sensitivity of a spiking neural network model ,
Journal of Statistical Physics, 22 (4), 800-808 (2018).
DOI : 10.1007/s10955-017-1948-y.
- Chevallier J., Duarte A., Löcherbach E., Ost G. :
Mean field limit for non linear spatially extended Hawkes processes with exponential memory kernels ,
Stochastic Processes and their Applications, to appear.
DOI : 10.1016/j.spa.2018.02.007.
- Chevallier J. :
Uniform decomposition of probability measures: quantization, clustering and rate of convergence ,
Journal of Applied Probability, 55 (4), 1037-1045 (2018).
DOI : 10.1017/jpr.2018.69.
- Chevallier J. et al. :
Network of interacting neurons with random synaptic weights ,
ESAIM: Proceedings and Surveys, EDP Sciences, 65, 445-475 (2019).
DOI : 10.1051/proc/201965445.
- Chevallier J. and Ost G. :
Fluctuations for Spatially Extended Hawkes Processes ,
Stochastic Processes and their Applications, 130 (9), 5510-5542 (2020).
DOI : 10.1016/j.spa.2020.03.015.
- Chevallier J., Melnykova A. and Tubikanec I. :
Diffusion approximation of multi-class Hawkes processes: Theoretical and numerical analysis
,
Advances in Applied Probability, 53 (9), 716-756 (2021).
DOI : 10.1017/apr.2020.73.
Preprints/Thesis
- Chevallier J. :
Uniform in time modulus of continuity of Brownian motion
.
- Chevallier J., Löcherbach E., Ost G. :
Inferring the dependence graph density of binary graphical models in high dimension
. Package MeanFieldGraph.jl.
- Master degree thesis (in french):
Détection de motifs de dépendance entre neurones
. - PhD Thesis :
Modelling large neural networks via Hawkes processes .
- Chevallier J.:
Approximation par champ-moyen : le couplage à la Sznitman pour les nuls. .
Complementary notes (in french).
Popularization articles
- Nos neurones se synchronisent-ils ? (in french), Images des Mathématiques, with P. Reynaud-Bouret.
Short talks (incomplete list)
- Microscopic approach of a time elapsed model
.
- Detection of dependence patterns with delay
.
- Spiking neural models: from point processes to partial differential equations
.
- Modelling large neural networks via Hawkes processes
(PhD defense).
- Spatial Hawkes as spike train model (with KMT coupling)
.
-
Mean field inference for an excitatory/inhibitory network
.
