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).
Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field / G. Gaeta. - In: OPEN COMMUNICATIONS IN NONLINEAR MATHEMATICAL PHYSICS. - 1:(2021), pp. 128-163. [10.46298/ocnmp.7535]
Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field
G. Gaeta
Primo
2021
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).
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