PROPAGATION OF CHAOS FOR STOCHASTIC SPATIALLY STRUCTURED NEURONAL NETWORKS WITH DELAY DRIVEN BY JUMP DIFFUSIONS

• 成果类型: Article
• 署名作者: Mehri, Sima; Scheutzow, Michael; Stannat, Wilhelm; Zangeneh, Ian Z.
• 署名单位: Technical University of Berlin; Sharif University of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1499
• 发表日期: 2020
• 页码: 175-207
• 关键词: differential-equations driven; EXISTENCE; limit

摘要

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.