About one unsolved problem in asymptotic p-stability of stochastic systems with delay

Abstract

The problem of asymptotic $ p $-stability for a linear differential equation with delay and stochastic perturbations, described by a set of mutually independent standard Wiener processes and the Poisson measure, is considered. It is shown the solution of this stability problem for some particular cases of the considered stochastic delay differential equation. However, for the general case of the considered equation, the proposed problem remains open and is presented to the attention of potential readers.

Keywords

• stochastic perturbations
• white noise
• poisson's jumps
• asymptotic $ p $-stability
• stability in probability
• general method of lyapunov functionals construction