Multi-class oscillating systems of interacting neurons

Susanne Ditlevsen and Eva Löcherbach

Stochastic Processes and their Applications, 2017, vol. 127, issue 6, 1840-1869

Abstract: We consider multi-class systems of interacting nonlinear Hawkes processes modeling several large families of neurons and study their mean field limits. As the total number of neurons goes to infinity we prove that the evolution within each class can be described by a nonlinear limit differential equation driven by a Poisson random measure, and state associated central limit theorems. We study situations in which the limit system exhibits oscillatory behavior, and relate the results to certain piecewise deterministic Markov processes and their diffusion approximations.

Keywords: Multivariate nonlinear Hawkes processes; Mean-field approximations; Piecewise deterministic Markov processes; Multi-class systems; Oscillations; Diffusion approximation (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (18)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:6:p:1840-1869

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DOI: 10.1016/j.spa.2016.09.013

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