Propagation of chaos for stochastic spatially structured neuronal networks with delay driven by jump diffusions

DOI10.1214/19-AAP1499zbMath1434.60299arXiv1805.01654MaRDI QIDQ2180382

Sima Mehri, Wilhelm Stannat, Bian Z. Zangeneh, Michael K. R. Scheutzow

Publication date: 13 May 2020

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.01654

zbMATH Keywords

propagation of chaosmonotone coefficientsmean-field limitsMckean-Vlasov equationsfully path dependent delayspatially structured neural networks

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Neural networks for/in biological studies, artificial life and related topics (92B20) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

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Cites Work

• Clarification and complement to ``Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and Fitzhugh-Nagumo neurons
• Numerical solutions of stochastic differential delay equations with Poisson random measure under the generalized Khasminskii-type conditions
• Stochastic partial differential equations: an introduction
• Spatially extended networks with singular multi-scale connectivity patterns
• Mean field limit for disordered diffusions with singular interactions
• Existence of global solutions and invariant measures for stochastic differential equations driven by Poisson type noise with non-Lipschitz coefficients
• Erratum to: ``Propagation of chaos in neural fields
• Existence and stability of solutions to non-Lipschitz stochastic differential equations driven by Lévy noise
• Limits and dynamics of stochastic neuronal networks with random heterogeneous delays
• On Wiener-Poisson type multivalued stochastic differential equations with non-Lipschitz coefficients
• Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons
• Limits and dynamics of randomly connected neuronal networks
• Existence and uniqueness of solutions of stochastic functional differential equations
• McKean–Vlasov limit for interacting systems with simultaneous jumps

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