Strong error bounds for the convergence to its mean field limit for systems of interacting neurons in a diffusive scaling-Reference-Cited by-同舟云学术

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Strong error bounds for the convergence to its mean field limit for systems of interacting neurons in a diffusive scaling

Published:2023-10-01 Issue:5 Volume:33 Page:
ISSN:1050-5164
Container-title:The Annals of Applied Probability
language:
Short-container-title:Ann. Appl. Probab.

Author:

Erny Xavier¹,Löcherbach Eva²,Loukianova Dasha³

Affiliation:

1. Ecole Polytechnique, Centre de mathématiques appliquées (CMAP)

2. Statistique, Analyse et Modélisation Multidisciplinaire, Université Paris 1 Panthéon-Sorbonne, EA 4543

3. Laboratoire de Mathématiques et Modélisation d’Évry, Université d’Évry Val d’Essonne, UMR CNRS 8071

Publisher

Institute of Mathematical Statistics

Subject

Statistics, Probability and Uncertainty,Statistics and Probability

Reference15 articles.

1. GALVES, A. and LÖCHERBACH, E. (2013). Infinite systems of interacting chains with memory of variable length—a stochastic model for biological neural nets. J. Stat. Phys. 151 896–921.

2. KURTZ, T. G. (1977/78). Strong approximation theorems for density dependent Markov chains. Stochastic Process. Appl. 6 223–240.

3. BRÉMAUD, P. (2020). Point Process Calculus in Time and Space. Springer.

4. CHEVALLIER, J., MELNYKOVA, A. and TUBIKANEC, I. (2021). Diffusion approximation of multi-class Hawkes processes: Theoretical and numerical analysis. Adv. in Appl. Probab. 53 716–756.

5. CORMIER, Q., TANRÉ, E. and VELTZ, R. (2020). Long time behavior of a mean-field model of interacting neurons. Stochastic Process. Appl. 130 2553–2595.

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1. Fluctuations for mean field limits of interacting systems of spiking neurons;Annales de l'Institut Henri Poincaré, Probabilités et Statistiques;2024-05-01

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