1205.2400 (David Aristoff)

Estimating Small Probabilities for Langevin Dynamics    [PDF]

David Aristoff

The problem of estimating small transition probabilities for overdamped Langevin dynamics is considered. A simplification of Girsanov's formula is obtained in which the relationship between the infinitesimal generator of the underlying diffusion and the change of probability measure corresponding to a change in the potential energy is made explicit. From this formula an asymptotic expression for transition probability densities is derived. Separately the problem of estimating the probability that a small noise Langevin process excapes a potential well is discussed.

View original: http://arxiv.org/abs/1205.2400