In this paper, the event-based control problems for nonlinear stochastic systems are investigated. First, a novel condition for stochastic input-to-state stability is established. Then, the dynamic event-triggered control approach is proposed and the stochastic stability of the resulting closed-loop system is also proved. Next, a new dynamic self-triggering mechanism is developed and the additional internal dynamic variable is designed according to the predicted value of the system state and error, which ensures that the closed-loop system is stochastically stable. It is shown that the lower bounds of interexecution times by the proposed dynamic event-triggered and self-triggered control approaches are all larger than zero, and the so-called Zeno phenomenon is avoided. Compared with the static event-triggering and self-triggering results, the interexecution times by the proposed dynamic approaches are prolonged on the whole. Two simulation examples are provided to show the efficiency of the proposed approaches.