2022 - T1 - WS2 - Mathematical modeling and statistical analysis in neuroscience

Collection 2022 - T1 - WS2 - Mathematical modeling and statistical analysis in neuroscience

Organizer(s) Ditlevsen, Susanne ; Faugeras, Olivier ; Galves, Antonio ; Reynaud-Bouret, Patricia ; Salort, Delphine ; Shinomoto, Shigeru

Date(s) 31/01/2022 - 04/02/2022

linked URL https://indico.math.cnrs.fr/event/6532/

00:00:00 / 00:00:00

16 30

Fluctuation limits for mean-field interacting nonlinear Hawkes processes

By Wilhelm Stannat

We investigate the asymptotic behavior of networks of interacting nonlinear Hawkes processes modelling a homogeneous population of neurons in the large population limit. In particular, we prove a functional central limit theorem for the mean spike-activity, thereby characterizing the asymptotic fluctuations in terms of a stochastic Volterra integral equation. Our approach differs from the usual approach via tightness of the associate martingale problem. Instead, we make use of the resolvent of the associated Volterra integral equation in order to represent fluctuations as Skorokhod continuous mappings of weakly converging martingales. Since the Lipschitz properties of the resolvent are explicit, our analysis in principle also allows to derive approximation errors in terms of driving martingales. We also discuss extensions of our results to multi-class systems.

The talk is based on joint work with S. Heesen.

Information about the video

Date of recording 02/02/2022
Date of publication 02/02/2022
Institution IHP
Language English
Audience Researchers
Director(s) Mandarine Audiovisuel
Format MP4
Venue IHP - Hermite Amphitheater

Citation data

DOI 10.57987/IHP.2022.T1.WS2.016
Cite this video Stannat, Wilhelm (02/02/2022). Fluctuation limits for mean-field interacting nonlinear Hawkes processes. IHP. Audiovisual resource. DOI: 10.57987/IHP.2022.T1.WS2.016
URL https://dx.doi.org/10.57987/IHP.2022.T1.WS2.016

Bibliography

S. Heesen, W. Stannat / Fluctuation limits for mean-field interacting nonlinear Hawkes processes. Stochastic Process. Appl., vol. 139 (2021), p. 280–297.

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

All the collection videos

58:30

published on January 31, 2022

Retrieving the structure of probabilistic sequences of auditory stimuli from electroencephalographic (EEG) signals

By Claudia Vargas , Guilherme Ost

34:36

published on January 31, 2022

Inferring monosynaptic connections from a cross-correlogram of neuronal spike trains

By Shigeru Shinomoto

38:18

published on January 31, 2022

Marked Point Process Modeling and Estimation Problems in Neural Data Analysis

By Uri Eden

47:44

published on January 31, 2022

Neural networks in the replica-mean field limits

By Thibault Taillefumier

25:17

published on January 31, 2022

Statistical Models of Interaction Across Brain Regions from Multi-Electrode Recordings

By Rob Kass

23:58

published on February 1, 2022

Self-organized criticality hierarchical modular networks of Galves-Löcherbach neurons

By Flavio Rusch

18:59

published on February 1, 2022

A new method to simulate Hawkes processes

By Tien Cuong Phi

24:46

published on February 1, 2022

Maximally predictive ensemble dynamics from data

By Antonio Carlos Costa

32:25

published on February 1, 2022

Multi-scale modeling of vesicular release at neuronal synapses

By Claire Guerrier

53:45

published on February 1, 2022

Graph rules and topological insights for inhibitory network dynamics

By Carina Curto

01:06:27

published on February 1, 2022

Topological insights on neuronal morphologies

By Lida Kanari , Kathryn Hess

22:56

published on February 2, 2022

Neural fields with rebound currents: novel routes to patterning

By Sunil Modhara

24:30

published on February 2, 2022

Beyond Blow-Up for Nonlinear Noisy Leaky Integrate and Fire neuronal models: numerical approach to the "plateau" state

By Alejandro Ramos Lora

01:01:45

published on February 2, 2022

System of interacting neurons with short term synaptic facilitation

By Eva Löcherbach , Christophe Pouzat

38:38

published on February 2, 2022

Spontaneous oscillations in a pure excitatory mean field networks of neurons

By Etienne Tanré

39:59

published on February 2, 2022

Fluctuation limits for mean-field interacting nonlinear Hawkes processes

By Wilhelm Stannat

28:14

published on February 2, 2022

Some recent results on a mean field of a network of 2d spiking neurons

By Romain Veltz

20:52

published on February 3, 2022

Time averages of a metastable system of spiking neurons

By Morgan André

21:23

published on February 3, 2022

Metastable spiking networks in the replica-mean-field limit

By Luyan Yu

25:10

published on February 3, 2022

Propagation of Chaos and Poisson Hypothesis for Replica Mean-Field Models

By Michel Davydov

01:03:32

published on February 3, 2022

Understanding Synaptic Mechanisms: Why a Multi-disciplinary Approach is Important

By Afia Ali , Mathieu Desroches

44:59

published on February 3, 2022

Projection methods for spatially-extended neurobiological models

By Daniele Avitabile

41:44

published on February 3, 2022

Front initiation in continuous neural fields

By Grégory Faye

41:50

published on February 3, 2022

Noise-driven bifurcations in a neural field system modelling networks of grid cells

By José A. Carillo

38:03

published on February 3, 2022

The non linear dynamics of retinal waves

By Bruno Cessac

24:34

published on February 4, 2022

Towards understanding the time periodic solutions in a kinetic model for neuron networks

By Zhennan Zhou

24:01

published on February 4, 2022

Theoretical study of the emergence of periodic solutions for the inhibitory NNLIF neuron model with synaptic delay

By Kota Ikeda

25:03

published on February 4, 2022

A multiple time renewal equation for neural assemblies with elapsed time model

By Nicolas Torres

20:29

published on May 7, 2024

A new synaptic rule to unify experimental heterogeneity

By Yuri Rodrigues

44:26

published on May 7, 2024

A neural mass model for abnormal beta-rebound in schizophrenia

By Stephen Coombes , Peter Liddle

Copyright Carmin.tv 2024

Give feedback