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An approach for the safety assessment of planned trajectories of autonomous vehicles is presented. Due to the unsafe nature of road traffic, the proposed safety assessment is performed in a probabilistic setting, where the probability distributions of possible future positions of traffic participants are computed based on dynamic models. The underlying algorithms have to be efficient as they need to provide a safety level of the currently planned path while the vehicle is in operation. In order to achieve the necessary efficiency of computation, the dynamics of traffic participants is abstracted into Markov-chains. The approach considers vehicle dynamics, interaction between traffic participants, and lane changes in multi-lane traffic.