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

This paper considers a class of nonlocal stochastic differential equations with time-varying delay whose coefficients are dependent on the pth 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.