Some Properties of an Algebraic Representation of Stochastic Processes
Paul W. Holland · The Annals of Mathematical Statistics · 1968
Heller's (1965) concept of a stochastic module is examined with the purpose of seeing what are the algebraic implications of various probabilistic properties of discrete time, finite state processes. $k$th order Markovity, recurrence, stationarity, and ergodicity are given characterizations in terms of the stochastic module.