Word combinatorics for stochastic differential equations: splitting integrators

2018/04/26 by A. Alamo, Alamo, A., J. M. Sanz‐Serna +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1804.09974

openalex publication_date 2018/04/26 · openalex created_date 2018/05/07 · openalex updated_date 2026/07/28

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.

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