A probabilistic theory of random maps (Q1776788)

The forward and backward Kolomogorov equations and the Fokker-Planck equation, resp., characterize transition probabilities and invariant measures, resp., for Markov semigroups with continuous time. Often they are invoked for the investigation of stochastic differential equations. The paper suggests an analogue of the forward and backward Kolmogorov equations and of the Fokker-Planck equation for certain classes of random maps, defining discrete time Markov chains. For this purpose, equations satisfied by transition probabilities are expanded in Taylor series. Numerically obtained results illustrate the quantities for certain one- and two-dimensional maps. For earlier work in this context see also \textit{R. F. Pawula} [IEEE Trans. Inf. Theory 13, 33--41 (1967; Zbl 0154.42401)].