Abstract

There is a wealth of methods to bound the distance between probability laws. However, when we want to compare two laws conditioned on the outcome of some random experiment, several difficulties arise. On the one hand, conditioning introduces strong dependence between the different components of a model, and most of the methods work well in a regime of weak dependence. However, quite surprisingly, there are also many situations when very different laws have similar, or even identical conditional distributions. In this talk, we discuss the basic ideas of a general procedure to adapt Stein’s method to bound the distance between conditional distributions and present two fundamental applications, where conditional laws arise naturally: the case of random walk bridges and the filtering equation. Joint work with A. Chiarini (ETH Zurich) and G. Conforti (École Polytechnique).​