Artificial neural networks (ANNs) are widely used as "black-box" models of complex processes and systems. Although the neural network simulation of deterministic processes is a well-known area, ANN simulation of stochastic ones is still at the frontier of the ANN methodology. In the current work, the method of ANN simulation of δ-correlated stochastic signals is proposed. The main advantage of the scheme is the utilization of a standard multilayer perceptron instead of complex stochastic ANN structures. The network receives input parameters of simulation together with basic random values and generates the desired stochastic signal.