Necessary and sufficient conditions of asymptotic mean square stability for stochastic linear difference equations Original Research Article

Many processes in automatic regulation, physics, mechanics, biology, economy, ecology, etc. can be modelled by hereditary systems (see, e.g., [1–4]). One of the main problems for the theory of such systems and their applications is connected with stability (see, e.g., [2–4]). Many stability results were obtained by the construction of appropriate Lyapunov functionals. At present, the method is proposed which allows us, in some sense, to formalize the procedure of the corresponding Lyapunov functionals construction [5–10]. In this work, by virtue of the proposed procedure, the necessary and sufficient conditions of asymptotic mean square stability for stochastic linear difference equations are obtained.