## The Annals of Probability

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

Arif Zaman

#### 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

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