Infinite dimensional stochastic differential equation models for spatially distributed neurons
type: Item
instance of: scholarly article
title: Infinite dimensional stochastic differential equation models for spatially distributed neurons
zbMATH Open document ID: 0565.60055
DOI: 10.1007/BF01449039
author: Gopinath Kallianpur
author: Robert L. Wolpert
published in: Applied Mathematics and Optimization
publication date: 1984-01-01T00:00:00Z
review text: A stochastic dynamic model for the membrane potential of spatially distributed neurons is investigated. In this model the voltage potential is given by the solution of a stochastic differential equation in a nuclear space in which the ''noise'' or driving term is a generalized Poisson process. The authors then consider a sequence of such generalized Poisson noises which converge to a Gaussian noise process and establish the weak convergence of the corresponding solutions of the stochastic differential equations in the sense of weak convergence of probability measures on the Skorohod space \(D(R^+;H_{-q})\), where \(H_{-q}\) is an appropriate Hilbert space.
reviewed by: Donald A. Dawson
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60B10
zbMATH DE Number: 3901763
zbMATH Keywords: membrane potential of spatially distributed neurons
zbMATH Keywords: weak convergence
Wikidata QID: Q115393505
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01449039
OpenAlex ID: W2020278217
description: scientific article; zbMATH DE number 3901763