An elementary proof for an extended version of the Choquet-Deny theorem. (English) Zbl 0732.60009
Authors’ 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 applied topics, the new result and its proof appear to be worth reporting.
Reviewer: D. Plachky (Münster)
MSC:
| 60B10 | Convergence of probability measures |
| 60G05 | Foundations of stochastic processes |
| 60E05 | Probability distributions: general theory |
| 60F20 | Zero-one laws |
Keywords:
Choquet-Deny theorem; exchangeable random variables; Hewitt-Savage zero-one law; martingale convergence theoremReferences:
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