Stochastic differential equation models for spatially distributed neurons and propagation of chaos for interacting systems.
Distribution or nuclear space-valued stochastic differential equations (SDEs) (diffusions as well as discontinuous equations) are discussed as stochastic models for the behavior of voltage potentials of spatially distributed neurons. A propagation of chaos result is obtained for an interacting system of Hilbert space-valued SDEs.
Kallianpur
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Department of Statistics, University of North Carolina, Chapel Hill 27599-3260.
D000818:Animals; D004594:Electrophysiology; D008959:Models, Neurological; D015233:Models, Statistical; D009415:Nerve Net / Q000166:cytology / Q000502:physiology; D009474:Neurons / Q000502:physiology*; D016012:Poisson Distribution; D013269:Stochastic Processes