abstract:
Transition path sampling is concernd with sampling from the distribution of the solution of an SDE, conditioned on the value of its endpoint. The case where the drift of this SDE is given by a gradient of a potential is studied in detail in works of M. Hairer, A. Stuart and J. Voss. The main idea is to find a process on path space which has the wanted distribution as (unique) invariant measue.
The used techniques do not apply in the non-gradient case which is left as an open problem, but a Dirichlet form approach allows us to construct a process on path-space which is reversible with respect to the distribution of the SDE (conditioned on the value of endpoint) even in the non-gradient setting. |