A new algorithm to compute long time molecular dynamics trajectories is presented. The technique is based on the stochastic path integral of Onsager and Machlup. Trajectories of fixed length of time are computed by path optimization between two end points. Modes of motion with periods shorter than the discrete time step are automatically filtered out, making the trajectories stable for almost an arbitrary time step. Several numerical examples are provided, including motions on the Mueller potential and a conformational transition in alanine dipeptide. Paths similar to the usual molecular dynamics trajectories are obtained, employing time steps 100 times larger than those used in straightforward molecular dynamics.