AIS data streams provide new means for maritime traffic surveillance. The massive amount of data as well as the irregular time sampling and the noise are the main factors that make it difficult to design automatic tools and models for AIS data analysis. In this work, we propose a deep learning model for AIS data using a stream-based architecture, which reduces storage redundancies and computational requirements. To deal with noisy and irregularly-sampled data, we explore variational recurrent neural networks. We empirically evaluate the performance of the proposed deep learning architecture for a three-task setting, referring respectively to vessel trajectory reconstruction, abnormal behaviour detection and vessel type identification on a real AIS dataset.