Quadratics in Markov-Chain Frequencies, and the Binary Chain of Order 2

Abstract

Letnrbe the frequency of the staterin a segment of a regular ergodic Markov chain. It is shown how to obtain the asymptotic distribution of any quadratic expression in thenr's. The method is especially convenient where the Markov chain is produced by a random motion on a circle. An explicit formula is given for the asymptotic variance of the number of 0's in a binary Markov chain of order 2.