In this paper, we introduce a framework for on-line learning of handwritten symbols from scratch. As such, learning suffers from missing data at the beginning of the learning process, in this paper we propose the use of Sigma-lognormal model to generate synthetic data. Our framework deals with a real-time use of the system, where the recognition of a single symbol cannot be postponed by the generation of synthetic data. We evaluate the use of our framework and Sigma-lognormal model by comparison of the recognition rate to a block-learning and learning without any synthetic data. Experimental results show that both of these contributions represent an enhancement to the on-line handwriting recognition, especially when starting from scratch.