Propagation of Chaos for Stochastic Spatially Structured Neuronal Networks with Delay driven by Jump Diffusions
Probability
2020-02-28 v3
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.
Keywords
Cite
@article{arxiv.1805.01654,
title = {Propagation of Chaos for Stochastic Spatially Structured Neuronal Networks with Delay driven by Jump Diffusions},
author = {Sima Mehri and Michael Scheutzow and Wilhelm Stannat and Bijan Z. Zangeneh},
journal= {arXiv preprint arXiv:1805.01654},
year = {2020}
}
Comments
In this version, a shorter title has been chosen. The manuscript has been accepted for publication in Annals of Applied Probability