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

ocnmp:7535 - Open Communications in Nonlinear Mathematical Physics, November 16, 2021, Volume 1 - https://doi.org/10.46298/ocnmp.7535
Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field

Authors: Giuseppe Gaeta

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).

Volume: Volume 1
Published on: November 16, 2021
Accepted on: November 14, 2021
Submitted on: June 2, 2021
Keywords: Mathematical Physics

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