A technique for studying strong and weak local errors of splitting stochastic integrators

2016/01/27 by A. Alamo, Alamo, A., J. M. Sanz‐Serna +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1601.07335

openalex publication_date 2016/01/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present a technique, based on so-called word series, to write down in a systematic way expansions of the strong and weak local errors of splitting algorithms for the integration of Stratonovich stochastic differential equations. Those expansions immediately lead to the corresponding order conditions. Word series are similar to, but simpler than, the B-series used to analyze Runge-Kutta and other one-step integrators. The suggested approach makes it unnecessary to use the Baker-Campbell-Hausdorff formula. As an application, we compare two splitting algorithms recently considered by Leimkuhler and Matthews to integrate the Langevin equations. The word series method bears out clearly reasons for the advantages of one algorithm over the other.

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