Stochastic differential equation models for spatially distributed neurons and propagation of chaos for interacting systems
type: Item
instance of: scholarly article
title: Stochastic differential equation models for spatially distributed neurons and propagation of chaos for interacting systems
zbMATH Open document ID: 0777.92004
DOI: 10.1016/0025-5564(92)90024-Q
author: Gopinath Kallianpur
published in: Mathematical Biosciences
publication date: 1993-06-29T00:00:00Z
review text: The aims of this paper are (1) to present a discussion of the stochastic partial differential equations and the infinite-dimensional stochastic differential equations that model the behavior of the membrane potential of spatially distributed neurons and (2) to study the asymptotic behavior of assemblies of interacting neurons. The stochastic cable equation models are summarized in the second part of this article. Distribution or nuclear space -- valued stochastic differential equations are introduced in the next section. Both cases, diffusion as well as discontinuous, are considered. The fourth section is devoted to propagation of chaos obtained for an interacting system of Hilbert space -- valued stochastic differential equations. A coupled pair of stochastic cable equations, introduced in the first part of this paper, is studied in its final part.
Mathematics Subject Classification ID: 92C20
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 219745
zbMATH Keywords: distribution-valued stochastic differential equations
zbMATH Keywords: infinite- dimensional stochastic differential equations
zbMATH Keywords: membrane potential of spatially distributed neurons
zbMATH Keywords: asymptotic behavior of assemblies of interacting neurons
zbMATH Keywords: stochastic cable equation models
zbMATH Keywords: nuclear space- valued stochastic differential equations
zbMATH Keywords: propagation of chaos
zbMATH Keywords: interacting system of Hilbert space-valued stochastic differential equations
reviewed by: Petr Lansky
MaRDI profile type: Publication
Wikidata QID: Q52408700
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full work available at URL: 0025-5564(92)90024-q
OpenAlex ID: W1992762171
description: scientific article; zbMATH DE number 219745