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We present a new method to sample conditioned trajectories of a systemevolving under Langevin dynamics, based on Brownian bridges. The trajectoriesare conditioned to end at a certain point (or in a certain region) in space.The bridge equations can be recast exactly in the form of a non linearstochastic integro-differential equation. This equation can be very wellapproximated when the trajectories are closely bundled together in space, i.e.at low temperature, or for transition paths. The approximate equation can besolved iteratively, using a fixed point method. We discuss how to choose theinitial trajectories and show some examples of the performance of this methodon some simple problems. The method allows to generate conditioned trajectorieswith a high accuracy.

Sampling constrained stochastic trajectories using Brownian bridges