Multi-class oscillating systems of interacting neurons

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Standard

Multi-class oscillating systems of interacting neurons. / Ditlevsen, Susanne; Löcherbach, Eva .

I: Stochastic Processes and Their Applications, Bind 127, 2017, s. 1840–1869.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Ditlevsen, S & Löcherbach, E 2017, 'Multi-class oscillating systems of interacting neurons', Stochastic Processes and Their Applications, bind 127, s. 1840–1869. https://doi.org/10.1016/j.spa.2016.09.013

APA

Ditlevsen, S., & Löcherbach, E. (2017). Multi-class oscillating systems of interacting neurons. Stochastic Processes and Their Applications, 127, 1840–1869. https://doi.org/10.1016/j.spa.2016.09.013

Vancouver

Ditlevsen S, Löcherbach E. Multi-class oscillating systems of interacting neurons. Stochastic Processes and Their Applications. 2017;127:1840–1869. https://doi.org/10.1016/j.spa.2016.09.013

Author

Ditlevsen, Susanne ; Löcherbach, Eva . / Multi-class oscillating systems of interacting neurons. I: Stochastic Processes and Their Applications. 2017 ; Bind 127. s. 1840–1869.

Bibtex

@article{e4b1e0c9a876482880f6e90e110d8322,
title = "Multi-class oscillating systems of interacting neurons",
abstract = "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.",
author = "Susanne Ditlevsen and Eva L{\"o}cherbach",
year = "2017",
doi = "10.1016/j.spa.2016.09.013",
language = "English",
volume = "127",
pages = "1840–1869",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier BV * North-Holland",

}

RIS

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