Abstract: The purpose of this talk is to describe some recent work (joint with Pedro Duarte and Joana Torres) where the technique of isospectral reduction, introduced by L. Bunimovich and B. Webb, is applied in the context of certain operators related to stochastic processes in order to show the existence of stationary measures and also get some approximations of the measure by means of the iteration of a dynamical procedure. We also want to discuss some possible new applications of the method.