A boundary theory approach to de Finetti's theorem

TL;DR

This paper applies boundary theory for transient Markov chains to provide a new proof of de Finetti's theorem, connecting stochastic process boundary concepts with exchangeability in probability.

Contribution

It introduces a boundary theory approach to de Finetti's theorem, offering a novel perspective and detailed proofs for the classical result.

Findings

Boundary theory effectively proves de Finetti's theorem

Provides detailed proofs of boundary theory concepts

Establishes a new link between Markov chains and exchangeability

Abstract

We show that boundary theory for transient Markov chains, as initiated by Doob, can be used to prove de Finetti's classical representation result for exchangeable random sequences. We also include the relevant parts of the theory, with full proofs.