Mean-Field Limit of a Stochastic Particle System Smoothly Interacting Through Threshold Hitting-Times and Applications to Neural Networks with Dendritic Component

DOI10.1137/140989042zbMath1325.60158arXiv1409.8221OpenAlexW2156937773MaRDI QIDQ3195479

James D. Inglis, Denis Talay

Publication date: 19 October 2015

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.8221

zbMATH Keywords

neural networkscable equationmean-field limitMcKean-Vlasov equationstochastic particle systemdendritic structurenoisy integrate-and-fire model

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Neural biology (92C20) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Vlasov equations (35Q83)

Related Items (11)

Rigorous Justification of the Fokker--Planck Equations of Neural Networks Based on an Iteration Perspective ⋮ Mean field dynamics of a Wilson–Cowan neuronal network with nonlinear coupling term ⋮ On a toy network of neurons interacting through their dendrites ⋮ Contagious McKean-Vlasov systems with heterogeneous impact and exposure ⋮ Uniqueness for contagious McKean–Vlasov systems in the weak feedback regime ⋮ Particle systems with singular interaction through hitting times: application in systemic risk modeling ⋮ An SPDE model for systemic risk with endogenous contagion ⋮ Mean field analysis of neural networks: a central limit theorem ⋮ Mean Field Analysis of Neural Networks: A Law of Large Numbers ⋮ Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons ⋮ Mean Field Limits of Particle-Based Stochastic Reaction-Diffusion Models

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