Probability metrics and recursive algorithms

It is shown by means of several examples that probability metrics are a useful tool to study the asymptotic behaviour of (stochastic) recursive algorithms. The basic idea of this approach is to find a .suitable' probability metric which yields contraction properties of the transformations describing the limits of the algorithm. In order to demonstrate the wide range of applicability of this contraction method we investigate examples from various fields, some of which have already been analysed in the literature.