On some basic features of strictly stationary, reversible Markov chains. (4th February 2021)

• Record Type: Journal Article
• Authors: Bradley, Richard C.
• Other Names: Bradley Richard C. guestEditor.; Davis Richard A. guestEditor.; Politis Dimitris N. guestEditor.
• Is Part Of: Journal of time series analysis. Volume 42:Number 5/6(2021)
• Page Start: 499
• Page End: 533
• Publication Date: 2021-02-04
• Subjects: Strictly stationary -- reversible Markov chain -- strong mixing -- spectral gap condition -- geometric ergodicity; Time-series analysis -- Periodicals; 519.232
• DOI: 10.1111/jtsa.12583
• Languages: English
• ISSNs: 0143-9782

Abstract

Abstract : It has been well known for some time that for strictly stationary Markov chains that are 'reversible', the special symmetry (with the distribution of the Markov chain as a whole being invariant under a reversal of the 'direction of time') provides special extra features in the mathematical theory. This article here is in part an exposition of some of the basic aspects of that special theory. The mathematical techniques employed in this review are relatively gentle, involving only some basic measure‐theoretic probability theory. To that special theory, a couple of new results are contributed here that are connected with the Rosenblatt strong mixing condition; and those new results in turn assist in bringing further clarity to the exposition of the theory.