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Estimating Small Probabilities for Langevin Dynamics

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arxiv 1205.2400 v2 pith:R6NQTMUX submitted 2012-05-10 math-ph math.MPphysics.comp-ph

David Aristoff This is my paper · ORCID
classification math-phmath.MPphysics.comp-ph
keywords estimatinglangevinprobabilitysmallchangedynamicsformulapotential
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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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Cited by 1 Pith paper

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  1. Benign Overfitting Does Not Occur in Diffusion Models

    stat.ML 2026-07 conditional novelty 7.0 of 10

    Benign overfitting and double descent do not occur in diffusion models: population and empirical score-matching losses cannot both be small without exponentially many samples.

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