Cheap arbitrary high order methods for single integrand SDEs
Numerical Analysis
2017-02-23 v2
Abstract
For a particular class of Stratonovich SDE problems, here denoted as single integrand SDEs, we prove that by applying a deterministic Runge-Kutta method of order we obtain methods converging in the mean-square and weak sense with order . The reason is that the B-series of the exact solution and numerical approximation are, due to the single integrand and the usual rules of calculus holding for Stratonovich integration, similar to the ODE case. The only difference is that integration with respect to time is replaced by integration with respect to the measure induced by the single integrand SDE.
Cite
@article{arxiv.1512.07342,
title = {Cheap arbitrary high order methods for single integrand SDEs},
author = {Kristian Debrabant and Anne Kværnø},
journal= {arXiv preprint arXiv:1512.07342},
year = {2017}
}