An elementary proof for an extended version of the Choquet-Deny theorem

Abstract

The Choquet-Deny theorem on an integral equation is extended using an elementary technique based on a certain inequality for exchangeable random variables. Previous proofs for partial results have involved amongst other things the Hewitt-Savage zero-one law and the martingale convergence theorem. In view of the importance of the Choquet-Deny theorem in stochastic processes and allied topics, the new result and its proof appear to be worth reporting.Choquet-Deny theorem Hewitt-Savage zero-one law exchangeable random variables integrated Cauchy equation renewal theorem martingale convergence theorem