Higher Strong Order Methods for It\^o SDEs on Matrix Lie Groups
Numerical Analysis
2021-02-09 v1 Numerical Analysis
Abstract
In this paper we present a general procedure for designing higher strong order methods for It\^o stochastic differential equations on matrix Lie groups and illustrate this strategy with two novel schemes that have a strong convergence order of 1.5. Based on the Runge-Kutta--Munthe-Kaas (RKMK) method for ordinary differential equations on Lie groups, we present a stochastic version of this scheme and derive a condition such that the stochastic RKMK has the same strong convergence order as the underlying stochastic Runge-Kutta method. Further, we show how our higher order schemes can be applied in a mechanical engineering as well as in a financial mathematics setting.
Cite
@article{arxiv.2102.04131,
title = {Higher Strong Order Methods for It\^o SDEs on Matrix Lie Groups},
author = {Michelle Muniz and Matthias Ehrhardt and Michael Günther and Renate Winkler},
journal= {arXiv preprint arXiv:2102.04131},
year = {2021}
}