AIS data streams provide new means for the monitoring and surveillance of the maritime traffic. 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 multi-task deep learning model for AIS data using a stream-based architecture, which reduces storage redundancies and computational requirements. To deal with noisy irregularly-sampled data, we explore variational recurrent neural networks. We demonstrate the relevance 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.