Tensor-based theory for quantized piecewise-affine Markov systems: Analysis of some map families

In this paper we consider a tensor-based approach to the analytical computa tion of higher-order expectations of quantized trajectories generated by Pi ecewise Affine Markov (PWAM) maps. We formally derive closed-form expressio ns for expectations of trajectories generated by three families of maps, re ferred to as (n, t)-tailed shifts, (n, t)-broken identities and (n, t, pi)- mixing permutations. These families produce expectations with asymptotic ex ponential decay whose detailed profile is controlled by map design. In the (n, t)-tailed shift case expectations are alternating in sign, in the (n, t )-broken identity case they are constant in sign, and the (n, t, pi)-mixing permutation case they follow a dumped periodic trend.