Multi-class oscillating systems of interacting neurons
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Multi-class oscillating systems of interacting neurons. / Ditlevsen, Susanne; Löcherbach, Eva .
In: Stochastic Processes and Their Applications, Vol. 127, 2017, p. 1840–1869.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Multi-class oscillating systems of interacting neurons
AU - Ditlevsen, Susanne
AU - Löcherbach, Eva
PY - 2017
Y1 - 2017
N2 - We consider multi-class systems of interacting nonlinear Hawkes processes modeling several large familiesof neurons and study their mean field limits. As the total number of neurons goes to infinity we provethat the evolution within each class can be described by a nonlinear limit differential equation driven bya Poisson random measure, and state associated central limit theorems. We study situations in which thelimit system exhibits oscillatory behavior, and relate the results to certain piecewise deterministic Markovprocesses and their diffusion approximations.
AB - We consider multi-class systems of interacting nonlinear Hawkes processes modeling several large familiesof neurons and study their mean field limits. As the total number of neurons goes to infinity we provethat the evolution within each class can be described by a nonlinear limit differential equation driven bya Poisson random measure, and state associated central limit theorems. We study situations in which thelimit system exhibits oscillatory behavior, and relate the results to certain piecewise deterministic Markovprocesses and their diffusion approximations.
U2 - 10.1016/j.spa.2016.09.013
DO - 10.1016/j.spa.2016.09.013
M3 - Journal article
VL - 127
SP - 1840
EP - 1869
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
ER -
ID: 181770548