To enable smooth and low-risk autonomous driving in the presence of other road users, such as cyclists and pedestrians, appropriate predictive safe speed control strategies relying on accurate and robust prediction models should be employed. However, difficulties related to driving scene understanding and a wide variety of features influencing decisions of other road users significantly complexifies prediction tasks and related driving. In support of that, this paper proposes hierarchical neural network (NN)-based prediction model of pedestrian crossing behavior, intended to be applied within an autonomous vehicle (AV) safe speed control strategy. Additionally, different single-level prediction models are proposed and analyzed as well to serve as a baseline. The hierarchical NN model is designed to predict the probability of pedestrian crossing the crosswalk prior to the vehicle at the high-level, and parameters of Gaussian probability distribution of pedestrian entry time to the crosswalk at the low-level. On the other hand, the baseline single-level models only provide entry time probability distributions, either in discrete form or in the form of bimodal Gaussian probability distribution. The proposed hierarchical model is validated against baseline ones for a simplified single-vehicle/single-pedestrian case, by using data obtained through large-scale simulations of a game theory-based pedestrian model and the vehicle being driven in an open-loop manner.