Asymptotics of a class of Markov processes which are not in general irreducible
Let \(\alpha_ n\) be a sequence of i.i.d. nondecreasing r.v.'s on a subset \(S\subset {\mathbb{R}}^ k \)into itself, and \(X_ 0\) be a r.v. with values in S independent of \(\alpha_ n\). The authors give conditions for the existence of unique invariant probabilities for the Markov processes \(X_ n\), defined by \(X_ n=\alpha_ n...\alpha_ 1X_ 0\). In addition, a functional central limit theorem is obtained. The authors provide two examples. The correction concerns an error in Lemma 2.2.
scientific article; zbMATH DE number 4064149