Numerical Approximations of Stochastic Differential Equations and
their Applications in Mathematical Neurosciences
Abstract
We provide a derivation of central limit theorems for Markov processes
arising in the approximation of stochastic differential equations.
We include extensions of the results obtained for continuous time processes
to the discrete time case with arbitrarily small step size.
A new energy interpretation of variance of the limit process is given.
In applications,
we provide a synaptically generated wave propagation model of theta-network
arising in Neurosciences. We show that a relatively large variance
of noise ( Markov chain and white noise) sustains the wave propagation
in the theta-network. We also investigate the continuous model of the
theta-network. Numerical simulations confirm the analysis of the
phenomena.
