{"docId":8712,"paperId":7535,"url":"https:\/\/ocnmp.episciences.org\/7535","doi":"10.46298\/ocnmp.7535","journalName":"Open Communications in Nonlinear Mathematical Physics","issn":"","eissn":"2802-9356","volume":[{"vid":443,"name":"Volume 1"}],"section":[],"repositoryName":"arXiv","repositoryIdentifier":"2106.00310","repositoryVersion":4,"repositoryLink":"https:\/\/arxiv.org\/abs\/2106.00310v4","dateSubmitted":"2021-06-02 11:31:38","dateAccepted":"2021-11-14 20:03:27","datePublished":"2021-11-16 11:46:18","titles":["Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field"],"authors":["Gaeta, Giuseppe"],"abstracts":["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).","Comment: 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"],"keywords":["Mathematical Physics"]}