Predictive control is a popular approach for further improving efficiency and performance of vehicular systems, enabling intelligent systems behavior appropriate to the driving situation. To calculate such control strategies, the future vehicle dynamics or subsequent states have to be predicted. We introduce a stochastic framework based on an explanatory model and stochastic processes to predict future vehicle dynamics with road network data. The distributions of the future states are approximated using sequential Monte Carlo simulation. The proposed approach enables stochastic forecasts incorporating uncertain driver behavior and available road data. Parameter inference is shown for exemplary real-drive test data and predictive performance is evaluated using commonly used reference models. The results show, that the explanatory model provides more specific information than time-series models do, still considering the uncertainty in the driver's behavior or the situation. The framework can be applied with predictive control algorithms, enabling intelligent control of vehicular systems. Furthermore, the framework or parts of it may be usable for other applications like predicting behavior of traffic participants or general characterization of driver behavior.