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

Arif Zaman
Source: Ann. Probab. Volume 14, Number 4 (1986), 1418-1427.

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).

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Primary Subjects: 60J05
Secondary Subjects: 60G10
Full-text: Open access