Translator Disclaimer
February 2020 Propagation of chaos for stochastic spatially structured neuronal networks with delay driven by jump diffusions
Sima Mehri, Michael Scheutzow, Wilhelm Stannat, Bian Z. Zangeneh
Ann. Appl. Probab. 30(1): 175-207 (February 2020). DOI: 10.1214/19-AAP1499

Abstract

Spatially structured neural networks driven by jump diffusion noise with monotone coefficients, fully path dependent delay and with a disorder parameter are considered. Well-posedness for the associated McKean–Vlasov equation and a corresponding propagation of chaos result in the infinite population limit are proven. Our existence result for the McKean–Vlasov equation is based on the Euler approximation that is applied to this type of equation for the first time.

Citation

Download Citation

Sima Mehri. Michael Scheutzow. Wilhelm Stannat. Bian Z. Zangeneh. "Propagation of chaos for stochastic spatially structured neuronal networks with delay driven by jump diffusions." Ann. Appl. Probab. 30 (1) 175 - 207, February 2020. https://doi.org/10.1214/19-AAP1499

Information

Received: 1 October 2018; Revised: 1 February 2019; Published: February 2020
First available in Project Euclid: 25 February 2020

zbMATH: 07200526
MathSciNet: MR4068309
Digital Object Identifier: 10.1214/19-AAP1499

Subjects:
Primary: 60K35, 92B20
Secondary: 60F99, 65C20, 82C80

Rights: Copyright © 2020 Institute of Mathematical Statistics

JOURNAL ARTICLE
33 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.30 • No. 1 • February 2020
Back to Top