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arXiv · 1205.2400

Estimating Small Probabilities for Langevin Dynamics

David Aristoff
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Abstract

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.

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David Aristoff. 2012-05-16. Estimating Small Probabilities for Langevin Dynamics. https://arxiv.org/abs/1205.2400

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