Stochastic differential equation models for spatially distributed neurons and propagation of chaos for interacting systems
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.
distribution-valued stochastic differential equations
infinite- dimensional stochastic differential equations
membrane potential of spatially distributed neurons
asymptotic behavior of assemblies of interacting neurons
nuclear space- valued stochastic differential equations
interacting system of Hilbert space-valued stochastic differential equations
scientific article; zbMATH DE number 219745
scientific article