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).

arXiv comment36 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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Cited by in corpus (2)

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