Infinite dimensional stochastic differential equation models for spatially distributed neurons
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.
membrane potential of spatially distributed neurons
scientific article; zbMATH DE number 3901763
scientific article