Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field
@article{Gaeta2021SymmetryOT,
title={Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field},
author={Giuseppe Gaeta},
journal={Open Communications in Nonlinear Mathematical Physics},
year={2021}
}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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References
SHOWING 1-10 OF 56 REFERENCES
Lunini, “Symmetry and integrability for stochastic differential equations
- J. Nonlin. Math. Phys
- 2018
Lunini, “On Lie-point symmetries for Ito stochastic differential equations
- J. Nonlin. Math. Phys. 24-S1
- 2017
Dynamical Theories of Brownian motion, Princeton UP 1967; 2 edition
- 2001
Reduction and reconstruction of SDEs via Girsanov and quasi Doob symmetries
- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2021
A reduction procedure for stochastic differential equations based on stochastic symmetries including Girsanov random transformations is proposed. In this setting, a new notion of reconstruction is…
Symmetry classification of scalar Ito equations with multiplicative noise
- MathematicsJournal of Nonlinear Mathematical Physics
- 2020
We provide a symmetry classification of scalar stochastic equations with multiplicative noise. These equations can be integrated by means of the Kozlov procedure, by passing to symmetry adapted…
Lie-point symmetries and stochastic differential equations: II
- Mathematics
- 2000
We complement the discussion of symmetries of Ito equations given in Gaeta and Rodriguez Quintero (1999 J. Phys. A: Math. Gen. 32 8485-505) by considering transformations acting on vector Wiener…
Symmetries of stochastic differential equations using Girsanov transformations
- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020
Aiming at enlarging the class of symmetries of a stochastic differential equation (SDE), we introduce a family of stochastic transformations able to change also the underlying probability measure…
Integration of the stochastic logistic equation via symmetry analysis
- MathematicsJournal of Nonlinear Mathematical Physics
- 2019
We apply the recently developed theory of symmetry of stochastic differential equations to a stochastic version of the logistic equation, obtaining an explicit integration, i.e. an explicit formula…
W-symmetries of Ito stochastic differential equations
- MathematicsJournal of Mathematical Physics
- 2019
We discuss W-symmetries of Ito stochastic differential equations, introduced in a recent paper by Gaeta and Spadaro [J. Math. Phys. 58, 053503 (2017)]. In particular, we discuss the general form of…
Symmetries of Itô stochastic differential equations and their applications
- MathematicsNonlinear Systems and Their Remarkable Mathematical Structures
- 2018