Stochastic differential equation models for spatially distributed neurons and propagation of chaos for interacting systems

DOI10.1016/0025-5564(92)90024-QzbMath0777.92004OpenAlexW1992762171WikidataQ52408700 ScholiaQ52408700MaRDI QIDQ1802897

Gopinath Kallianpur

Publication date: 29 June 1993

Published in: Mathematical Biosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0025-5564(92)90024-q

zbMATH Keywords

propagation of chaosmembrane potential of spatially distributed neuronsasymptotic behavior of assemblies of interacting neuronsdistribution-valued stochastic differential equationsinfinite- dimensional stochastic differential equationsinteracting system of Hilbert space-valued stochastic differential equationsnuclear space- valued stochastic differential equationsstochastic cable equation models

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Neural biology (92C20) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

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Consistency of Bayesian nonparametric inference for discretely observed jump diffusions ⋮ Approximation of solution of the cable equation driven by a stochastic measure

Cites Work

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• Infinite dimensional stochastic differential equation models for spatially distributed neurons
• Stochastic evolution equations driven by nuclear-space-valued martingales
• Propagation of chaos and the McKean-Vlasov equation in duals of nuclear spaces
• The response of a spatially distributed neuron to white noise current injection
• On interacting systems of Hilbert-space-valued diffusions
• Diffusion equations in duals of nuclear spaces
• A stochastic model of neural response
• The existence and uniqueness of solutions of nuclear space-valued stochastic differential equations driven by poisson random measures
• Linear Partial Differential Equations with Random Forcing

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