Local existence-uniqueness and continuation of solutions for delay stochastic evolution equations

Abstract

In this article, we consider dynamic behaviours of a class of non-linear delay stochastic evolution equations. Local existence and uniqueness of the solutions are obtained with the aid of proper iterative scheme and moment estimations. We also propose a continuation result and our results generalize the known results.

Keywords:

• stochastic evolution equations
• local existence
• uniqueness
• continuation

Acknowledgements

This work was partially supported by NNSF of China (Grant No. 10871077).