Stability criteria for a class of stochastic distributed delay systems

In the paper linear distributed delay stochastic systems are considered. Using theory of stochastic differential equations sufficient conditions for different kinds of stability are formulated and proved. The article attempts to generalise results presented in the paper [1] and thus theorems proved in [1] become a special case of a generalised approach. The considered class is wider - the function that influence dynamics of a problem can be a real solution of N-degree linear deterministic differential equation. Therefore the generalised reduction technique of distributed delay to lumped delay has to be applied. Criteria for numerous properties of the aforementioned class followed Mao theory designed for point delay systems [2, 3]