Volume 17, Issue 2, June 2010, Pages 179 - 196
A New Set of Admitted Transformations for Autonomous Stochastic Ordinary Differential Equations
Received 5 September 2009, Accepted 20 October 2009, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925110000702How to use a DOI?
- Keywords
- Brownian motion; Lie group of transformations; stochastic differential equation; admitted transformation; determining equations
- Abstract
This paper investigates symmetries of autonomous ordinary stochastic differential equations. Change of time includes the stochastic process itself, and is uniquely determined by the transformation of the spatial variable. As a particular feature, the time change by an admitted Lie symmetry group may be unrelated with the time change in the stochastic process. Sufficient conditions for a Lie group to be admitted by an autonomous equation are derived. This method can be applied to second order autonomous equations as well as systems of autonomous stochastic differential equations.
- Copyright
- © 2010 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 - Sergey V. Meleshko AU - Eckart Schulz PY - 2021 DA - 2021/01/07 TI - A New Set of Admitted Transformations for Autonomous Stochastic Ordinary Differential Equations JO - Journal of Nonlinear Mathematical Physics SP - 179 EP - 196 VL - 17 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110000702 DO - 10.1142/S1402925110000702 ID - Meleshko2021 ER -