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Randomness is natural - an introduction to regularisation by noise

Snapshots of modern mathematics from Oberwolfach

Randomness is natural - an introduction to regularisation by noise

Differential equations make predictions on the future state of a system given the present. In order to get a sensible prediction, sometimes it is necessary to include randomness in differential equations, taking microscopic effects into account. Surprisingly, despite the presence of randomness, our probabilistic prediction of future states is stable with respect to changes in the surrounding environment, even if the original prediction was unstable. This snapshot will unveil the core mathematical mechanism underlying this “regularisation by noise” phenomenon.

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Mathematical subjects

Probability Theory and Statistics

Connections to other fields

Chemistry and Earth Science
Physics

Author(s)

Ana Djurdjevac, Henri Elad Altman, Tommaso Rosati

License

DOI (Digital Object Identifier)

10.14760/SNAP-2024-002-EN

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snapshot-2024-002.pdf

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