Adaptive pinning synchronization of complex networks with stochastic perturbations.
Almost sure exponential stability of delayed cellular neural networks.
Almost sure subexponential decay rates of scalar Itô-Volterra equations.
An existence result to a strongly coupled degenerated system arising in tumor modeling.
Approximation of the Zakai equation in a nonlinear filtering problem with delay
A nonlinear filtering problem with delays in the state and observation equations is considered. The unnormalized conditional probability density of the filtered diffusion process satisfies the so-called Zakai equation and solves the nonlinear filtering problem. We examine the solution of the Zakai equation using an approximation result. Our theoretical deliberations are illustrated by a numerical example.
Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions [Book]
Asymptotic and exponential decay in mean square for delay geometric Brownian motion
We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions of the geometric Brownian motion with delay. The conditions are written in terms of the parameters and are explicit for the case of asymptotic decay. For exponential decay, they are easily resolvable numerically. The analytical method is based on construction of a Lyapunov functional (asymptotic decay) and a forward-backward estimate for the square mean (exponential decay).