Journal of Nonlinear Mathematical Physics

Volume 24, Issue Supplement 1, December 2017, Pages 90 - 102

On Lie-point symmetries for Ito stochastic differential equations

Authors
G. Gaeta*, , C. Lunini,
Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, 20133 Milano, Italy
Received 29 September 2017, Accepted 31 October 2017, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2017.1418056How to use a DOI?
Abstract

In the deterministic realm, both differential equations and symmetry generators are geometrical objects, and behave properly under changes of coordinates; actually this property is essential to make symmetry analysis independent of the choice of coordinates and applicable. When trying to extend symmetry analysis to stochastic (Ito) differential equations, we are faced with a problem inherent to their very nature: they are not geometrical object, and they behave in their own way (synthesized by the Ito formula) under changes of coordinates. Thus it is not obvious that symmetries are preserved under a change of coordinates. We will study when this is the case, and when it is not; the conclusion is that this is always the case for so called simple symmetries. We will also note that Kozlov theory relating symmetry and integrability for stochastic differential equations is confirmed by our considerations and results, as symmetries of the type relevant in it are indeed of the type preserved under coordinate changes.

Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
24 - Supplement 1
Pages
90 - 102
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2017.1418056How to use a DOI?
Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - G. Gaeta
AU  - C. Lunini
PY  - 2021
DA  - 2021/01/06
TI  - On Lie-point symmetries for Ito stochastic differential equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 90
EP  - 102
VL  - 24
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2017.1418056
DO  - https://doi.org/10.1080/14029251.2017.1418056
ID  - Gaeta2021
ER  -