## The Annals of Probability

- Ann. Probab.
- Volume 14, Number 4 (1986), 1418-1427.

### A Finite Form of De Finetti's Theorem for Stationary Markov Exchangeability

#### Abstract

De Finetti's theorem for stationary Markov exchangeability states that a sequence having a stationary and Markov exchangeable distribution is a mixture of Markov chains. A finite version of this theorem is given by considering a finite sequence $X_1,\ldots, X_n$ which is stationary and Markov exchangeable. It is shown that any portion of $k$ consecutive elements, say $X_1,\cdots, X_k$ for $k < n$, is nearly a mixture of Markov chains (the distance measured in the variation norm).

#### Article information

**Source**

Ann. Probab., Volume 14, Number 4 (1986), 1418-1427.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176992383

**Digital Object Identifier**

doi:10.1214/aop/1176992383

**Mathematical Reviews number (MathSciNet)**

MR866363

**Zentralblatt MATH identifier**

0608.60032

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60J05: Discrete-time Markov processes on general state spaces

Secondary: 60G10: Stationary processes

**Keywords**

de Finetti's theorem Markov exchangeability stationary processes Markov chains

#### Citation

Zaman, Arif. A Finite Form of De Finetti's Theorem for Stationary Markov Exchangeability. Ann. Probab. 14 (1986), no. 4, 1418--1427. doi:10.1214/aop/1176992383. https://projecteuclid.org/euclid.aop/1176992383