Unsolved problem about stability of stochastic difference equations with continuous time and distributed delay

Abstract

Despite the fact that the theory of stability of continuous-time difference equations has a long history, is well developed and very popular in research, there is a simple and clearly formulated problem about the stability of stochastic difference equations with continuous time and distributed delay, which has not been solved for more than 13 years. This paper offers to readers some generalization on this unsolved problem in the hope that it will help move closer to its solution.

Keywords

• Difference equations
• continuous time
• distributed delay
• stochastic perturbations
• asymptotic mean square quasistability