In the present study, we demonstrate the learning and recognition capabilities of our recently proposed recurrent neural network (RNN) model called stochastic continuous-time RNN (S-CTRNN). S-CTRNN can learn to predict not only the mean but also the variance of the next state of the learning targets. The network parameters consisting of weights, biases, and initial states of context neurons are optimized through maximum likelihood estimation (MLE) using the gradient descent method. First, we clarify the essential difference between the learning capabilities of conventional CTRNN and S-CTRNN by analyzing the results of a numerical experiment in which multiple fluctuating temporal patterns were used as training data, where the variance of the Gaussian noise varied among the patterns. Furthermore, we also show that the trained S-CTRNN can recognize given fluctuating patterns by inferring the initial states that can reproduce the patterns through the same MLE scheme as that used for network training.