Effect of noise on the solutions of non-linear delay systems

摘要

In this study the authors are concerned with the effect of noise on the solutions of a class of non-linear delay systems. The systems under investigation are non-linear without linear growth condition requirement, which makes the analysis difficult to ensure the existence and uniqueness of solutions. The authors first introduce a set of new non-linear growth conditions with delays, and then provide the existence and uniqueness of solutions as well as some properties of the solutions. The new condition only requires the knowledge of the coefficient of the highest term, which is much easier to check in practice than the traditional conditions. Finally, an example is given to show the effectiveness and potential of theoretic results obtained.