Path sampling with stochastic dynamics: Some new algorithms

We propose here some new sampling algorithms for path sampling in the case when stochastic dynamics are used. In particular, we present a new proposal function for equilibrium sampling of paths with a Monte-Carlo dynamics (the so-called "brownian tube" proposal). This proposal is based on the continuity of the dynamics with respect to the random forcing, and generalizes all previous approaches when stochastic dynamics are used. The efficiency of this proposal is demonstrated using some measure of decorrelation in path space. We also discuss a switching strategy that allows to transform ensemble of paths at a finite rate while remaining at equilibrium, in contrast with the usual Jarzynski like switching. This switching is very interesting to sample constrained paths starting from unconstrained paths, or to perform simulated annealing in a rigorous way.