Analysis of splitting methods for reaction-diffusion problems using stochastic calculus

We consider linear and nonlinear reaction-diffusion problems, and their time dis- cretization by splitting methods. We give probabilistic interpretations of the splitting schemes, and show how these representations allow to give error bounds for the deter- ministic propagator under weak hypothesis on the reaction part. To show these results, we only use the Itˆo formula, and basic properties of solutions of stochastic differential equations. Eventually, we show how probabilistic representations of splitting schemes can be used to derive "hybrid" numerical schemes based on Monte Carlo approxima- tions of the splitting method itself.