In Ambient Assisted Living (AAL), Activity Recognition (AR) plays a crucial role in filling the semantic gap between sensor data and interpretation needed at the application level. We propose a quantitative model-based approach to on-line prediction of activities that takes into account not only the sequencing of events but also the continuous duration of their inter-occurrence times: given a stream of time-stamped and typed events, online transient analysis of a continuous-time stochastic model is used to derive a measure of likelihood for the currently performed activity and to predict its evolution until the next event; while the structure of the model is predefined, its actual topology and stochastic parameters are automatically derived from the statistics of observed events. The approach is validated with reference to a public data set widely used in applications of AAL, providing results that show comparable performance with state-of-the-art offline approaches, namely Hidden Ma...