Stochastic Perturbation of Discrete Time Systems

We have seen two ways in which uncertainty (and thus probability) may appear in the study of strictly deterministic systems. The first was the consequence of following a random distribution of initial states, which, in turn, led to a development of the notion of the Frobenius-Perron operator and an examination of its properties as a means of studying the asymptotic properties of flows of densities. The second resulted from the random application of a transformation S to a system and led naturally to our study of the linear Boltzmann equations.