Symmetries of Stochastic Differential Equations: a geometric approach
Probability
2016-08-02 v1 Mathematical Physics
math.MP
Abstract
A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an algebra of strong symmetries for a modified SDE is proved under suitable regularity assumptions. This general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional Brownian motion.
Keywords
Cite
@article{arxiv.1512.05215,
title = {Symmetries of Stochastic Differential Equations: a geometric approach},
author = {Francesco C. De Vecchi and Paola Morando and Stefania Ugolini},
journal= {arXiv preprint arXiv:1512.05215},
year = {2016}
}