An analytic approach to the Markov chains recursive in the sense of Harris, and the Berry-Esseen estimate (Q1593981)

In Theorem~1, a Berry-Esseen bound is given to describe the rate of convergence to normality of \(\frac 1{\sqrt{n}}\sum_{k=0}^ng(X_k)\) as \(n\to\infty\), where \(X_0,X_1,\ldots\) is a Markov chain conditioned on \(X_0=x\) and \(g\) is a measurable real function. The dependence of the bound on the moments and transition probabilities is made explicit. The result complements the bound given by \textit{E. Bolthausen} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 60, 283-289 (1982; Zbl 0476.60022)]. The relations between the norming quantities of Theorem~1 and those in preceding works are made explicit in Theorems~2 and 3.