“…Stochastic differential delayed equations (SDDEs, for short) are nice tools to described the dynamics of some natural and social phenomena (see Mohammed [15,16]). Since then, massive research on related topics has become a desirable and serious endeavor among researchers in stochastic optimal control, differential games, mathematical finance and so on (see [17,21,2,18,32,3,9,10,6,28,34,30,12]). The forward SDDEs characterize the dynamic changes of state processes with given initial state trajectories.…”