Word combinatorics for stochastic differential equations: splitting integrators
Numerical Analysis
2018-04-27 v1 Combinatorics
Probability
Abstract
We present an analysis based on word combinatorics of splitting integrators for Ito or Stratonovich systems of stochastic differential equations. In particular we present a technique to write down systematically the expansion of the local error; this makes it possible to easily formulate the conditions that guarantee that a given integrator achieves a prescribed strong or weak order. This approach bypasses the need to use the Baker-Campbell-Hausdorff (BCH) formula and shows the existence of an order barrier of two for the attainable weak order. The paper also provides a succinct introduction to the combinatorics of words.
Cite
@article{arxiv.1804.09974,
title = {Word combinatorics for stochastic differential equations: splitting integrators},
author = {A. Alamo and J. M. Sanz-Serna},
journal= {arXiv preprint arXiv:1804.09974},
year = {2018}
}