Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field

Abstract

We classify simple symmetries for an Ornstein-Uhlenbeck process, describing a particle in an external force field $f(x)$. It turns out that for sufficiently regular (in a sense to be defined) forces there are nontrivial symmetries only if $f(x)$ is at most linear. We fully discuss the isotropic case, while for the non-isotropic we only deal with a generic situation (defined in detail in the text).

36 pages in OCNMP format, 27 pages in RevTex format. To appear in OCNMP (Open Communications in Nonlinear Mathematical Physics), see https://ocnmp.episciences.org

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• Symmetry of stochastic non-variational differential equations
• W-Symmetries of Ito stochastic differential equations
• Reduction and reconstruction of SDEs via Girsanov and quasi Doob symmetries
• Integration of the stochastic logistic equation via symmetry analysis
• Recent advances in symmetry of stochastic differential equations

Cited by in corpus (2)

• Symmetry classification of scalar autonomous Ito stochastic differential equations with simple noise
• Integrable Ito equations with multiple noises