Depending on driver intention and current motion state of vehicle, an infinite set of possible future trajectories exists. In this paper we present a stochastic filter which is able to select a representative set of reasonable trajectories from this solution set using additional information from a digital map. This is achieved by representing the map's traffic lanes by their corresponding centerlines. Each detected vehicle is projected on these centerlines, where the necessary information is modeled as a multivariate random variable. With this stochastic model of traffic lanes and the stochastic vector of vehicle detection we define a new stochastic residual vector, which is used both in the lane assignment and during the generation of the motion predictions. For each traffic lane, which is assigned as relevant for a detected vehicle, we generate a new motion hypothesis by using an Extended Kalman Filter. To assess the plausibility of each motion hypothesis we employ an adaptive multivariate MCUSUM algorithm. The implemented stochastic filter is tested by evaluating real data from the Ko-FAS Research Initiative. While traditional motion prediction based on previous and current motion states of a vehicle only provide plausible prediction for a short term time horizon, we show that our approach achieves a reasonable motion hypothesis for long prediction intervals especially in complex scenarios as road intersections.