  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.
