## The Annals of Mathematical Statistics

### A Characterisation of a Class of Functions of Finite Markov Chains

#### Abstract

In a previous paper ([2], Theorem 3.1) this author has given some sufficient conditions for a stationary process to be a function of a finite Markov chain. Suppose $\mathscr{F}$ denotes the class of functions which satisfy these conditions. In this paper we give a characterisation of $\mathscr{F}$. Using this characterisation $\mathscr{F}$ is shown to be wider than the class of regular functions of finite Markov chains.

#### Article information

Source
Ann. Math. Statist., Volume 36, Number 2 (1965), 524-528.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177700162

Digital Object Identifier
doi:10.1214/aoms/1177700162

Mathematical Reviews number (MathSciNet)
MR172333

Zentralblatt MATH identifier
0139.34602

JSTOR