About Some Unsolved Problems in the Stability Theory of Stochastic Differential and Difference Equations

This paper continues a series of papers devoted to unsolved problems in the theory of stability and optimal control for stochastic systems. A delay differential equation with stochastic perturbations of the white noise and Poisson’s jumps types is considered. In contrast to the known stability condition, in which it is assumed that stochastic perturbations fade on the infinity quickly enough, a new situation is studied, in which stochastic perturbations can fade on the infinity either slowly or not fade at all. Some unsolved problem in this connection is proposed to readers attention. Besides some unsolved problems of stabilization for one stochastic delay differential equation and one stochastic difference equation are also proposed.