Identification of nonlinear stochastic processes via differential neural networks is discussed. A new "dead-zone" type learning law for the weight dynamics is suggested. By a stochastic Lyapunov-like analysis the stability conditions for the identification error as well as for the neural network weights are established. The adaptive trajectory tracking using the obtained neural network model is realized for the subclass of stochastic completely controllable processes linearly dependent on control. The upper bounds for the identification and adaptive tracking errors are established,