We give a sketch of a theoretical framework aiming at a statistical description of discrete-time systems whose state space can be partitioned in regions among which the trajectories move in a Markov-like fashion. A constructive method is given to produce an analytical z-domain expression for the joint distribution of the system state at any number of observation instants. The availability of such tools should also ease the analysis of complex chaotic-maps with a possibly infinite description and exhibiting highly non-trivial statistical features.