Even the first iterate of a Markov operator is contracting in an \(L_ 2\) norm
The author investigates the relaxation toward the statistical equilibrium in the noisy maps \(x_{n+1} = f(x_n) + \zeta_n\), where \(\zeta\) is a random noise with distribution \(w(\zeta)\). A weighted \(L_2\) norm is introduced in which Markov operators (associated with noisy maps) are contracting provided the kernel is smooth enough. The significance of such norms for spatiotemporal chaos and random fields is discussed.
scientific article; zbMATH DE number 795353