Existence results and the moment estimate for nonlocal stochastic differential equations with time-varying delay

Abstract

This paper considers a class of nonlocal stochastic differential equations with time-varying delay whose coefficients are dependent on the p th moment. By applying the fixed point theorem, the existence and uniqueness of the solution of nonlocal stochastic differential delay equations is studied. Also, a class of moment estimates of solutions is considered. The results are a generalization and continuation of the recent results on this issue. An example is provided to illustrate the effectiveness of our results.