Geodesic
Spiking neurons : interacting Hawkes processes, mean field limits and oscillations
E. Löcherbach1
1 CNRS UMR 8088, Département de Mathématiques, Université de Cergy-Pontoise, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France. email :
ESAIM. Proceedings, Tome 60 (2017), pp. 90-103.

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This paper gives a short survey of some aspects of the study of Hawkes processes in high dimensions, in view of modeling large systems of interacting neurons. We first present a perfect simulation result allowing for a graphical construction of the process in infinite dimension. Then we turn to the study of mean field limits and show how in some cases the delays present in the Hawkes intensities give rise to oscillatory behavior of the limit process.
DOI : 10.1051/proc/201760090

E. Löcherbach 1

1 CNRS UMR 8088, Département de Mathématiques, Université de Cergy-Pontoise, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France. email : 
@article{EP_2017_60_a4,
     author = {E. L\"ocherbach},
     title = {Spiking neurons : interacting {Hawkes} processes, mean field limits and oscillations},
     journal = {ESAIM. Proceedings},
     pages = {90--103},
     publisher = {mathdoc},
     volume = {60},
     year = {2017},
     doi = {10.1051/proc/201760090},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201760090/}
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E. Löcherbach. Spiking neurons : interacting Hawkes processes, mean field limits and oscillations. ESAIM. Proceedings, Tome 60 (2017), pp. 90-103. doi : 10.1051/proc/201760090. http://geodesic.mathdoc.fr/articles/10.1051/proc/201760090/

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