A symmetry-adapted numerical scheme for SDEs
Probability
2020-08-04 v2 Numerical Analysis
Mathematical Physics
math.MP
Numerical Analysis
Abstract
We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry adapted coordinates system where the given SDE has notable invariant properties. An approximation scheme preserving the symmetry properties of the equation is introduced. Our algorithmic procedure is applied to the family of general linear SDEs for which two theoretical estimates of the numerical forward error are established.
Cite
@article{arxiv.1704.04167,
title = {A symmetry-adapted numerical scheme for SDEs},
author = {Francesco C. De Vecchi and Andrea Romano and Stefania Ugolini},
journal= {arXiv preprint arXiv:1704.04167},
year = {2020}
}
Comments
A numerical example added