John Appleby | Searcharxiv

arXiv2023

Mean square asymptotic stability characterisation of perturbed linear stochastic functional differential equations

In this paper we investigate the mean square asymptotic stability of a perturbed scalar linear stochastic functional differential equation. Specifically, we are able to give necessary and sufficient conditions on the forcing terms for convergence of the mean square, exponential convergence of the mean square, and integrability of the mean square of solutions. It is also essential that the underlying unperturbed SFDE is mean square asymptotically stable for these results to hold.

math.PR↗

arXiv2013

On limit periodicity of discrete time stochastic processes

We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found sufficient conditions for existence of a periodic process such that the solution converges to it, including almost surely convergence.

math.DS↗