  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.
