Propagation of chaos: a review of models, methods and applications. II. Applications
LP Chaintron, A Diez - arxiv preprint arxiv:2106.14812, 2021 - arxiv.org
The notion of propagation of chaos for large systems of interacting particles originates in
statistical physics and has recently become a central notion in many areas of applied …
statistical physics and has recently become a central notion in many areas of applied …
[HTML][HTML] Multi-class oscillating systems of interacting neurons
S Ditlevsen, E Löcherbach - Stochastic Processes and their Applications, 2017 - Elsevier
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 …
several large families of neurons and study their mean field limits. As the total number of …
Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues
A univariate Hawkes process is a simple point process that is self-exciting and has a
clustering effect. The intensity of this point process is given by the sum of a baseline intensity …
clustering effect. The intensity of this point process is given by the sum of a baseline intensity …
Renewal in Hawkes processes with self-excitation and inhibition
M Costa, C Graham, L Marsalle… - Advances in Applied …, 2020 - cambridge.org
We investigate the Hawkes processes on the positive real line exhibiting both self-excitation
and inhibition. Each point of such a point process impacts its future intensity by the addition …
and inhibition. Each point of such a point process impacts its future intensity by the addition …
An elapsed time model for strongly coupled inhibitory and excitatory neural networks
N Torres, MJ Cáceres, B Perthame, D Salort - Physica D: Nonlinear …, 2021 - Elsevier
The elapsed time model has been widely studied in the context of mathematical
neuroscience with many open questions left. The model consists of an age-structured …
neuroscience with many open questions left. The model consists of an age-structured …
[HTML][HTML] Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels
We consider spatially extended systems of interacting nonlinear Hawkes processes
modeling large systems of neurons placed in R d and study the associated mean field limits …
modeling large systems of neurons placed in R d and study the associated mean field limits …
Asymptotic behaviour of neuron population models structured by elapsed-time
We study two population models describing the dynamics of interacting neurons, initially
proposed by Pakdaman et al (2010 Nonlinearity 23 55–75) and Pakdaman et al (2014 J …
proposed by Pakdaman et al (2010 Nonlinearity 23 55–75) and Pakdaman et al (2014 J …
Non-exchangeable networks of integrate-and-fire neurons: spatially-extended mean-field limit of the empirical measure
PE Jabin, V Schmutz, D Zhou - arxiv preprint arxiv:2409.06325, 2024 - arxiv.org
The dynamics of exchangeable or spatially-structured networks of $ N $ interacting
stochastic neurons can be described by deterministic population equations in the mean-field …
stochastic neurons can be described by deterministic population equations in the mean-field …
Interacting Hawkes processes with multiplicative inhibition
In the present work, we introduce a general class of mean-field interacting nonlinear
Hawkes processes modeling the reciprocal interactions between two neuronal populations …
Hawkes processes modeling the reciprocal interactions between two neuronal populations …
Multivariate Hawkes processes on inhomogeneous random graphs
Z Agathe-Nerine - Stochastic Processes and their Applications, 2022 - Elsevier
We consider a population of N interacting neurons, represented by a multivariate Hawkes
process: The firing rate of each neuron depends on the history of the connected neurons …
process: The firing rate of each neuron depends on the history of the connected neurons …