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}
}
  • G. Gaeta
  • Published 1 June 2021
  • Mathematics
  • Open Communications in Nonlinear Mathematical Physics
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). 

Integrable autonomous scalar Ito equations with multiple noise sources

The classification of scalar Ito equations with a single noise source which admit a so called standard symmetry and hence are – by the Kozlov construction – integrable is by now complete. In this

Symmetry classification of scalar autonomous Ito stochastic differential equations with simple noise

This work provides a classification of scalar autonomous Ito stochastic differential equations with simple noise possessing symmetries, and extends previous classifications in that it also considers recently introduced types of symmetry, in particular standard random symmetry not considered in those.

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

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

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

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

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

  • G. Gaeta
  • Mathematics
    Journal 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

  • G. Gaeta
  • Mathematics
    Journal 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

  • N. Euler
  • Mathematics
    Nonlinear Systems and Their Remarkable Mathematical Structures
  • 2018
...