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Proceedings of the American Mathematical Society

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A short proof of the martingale convergence theorem


Author: Charles W. Lamb
Journal: Proc. Amer. Math. Soc. 38 (1973), 215-217
MSC: Primary 60G45
MathSciNet review: 0324770
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Abstract: The martingale convergence theorem is first proved for uniformly integrable martingales by a standard application of Doob's maximal inequality. A simple truncation argument is then given which reduces the proof of the $ {L^1}$-bounded martingale theorem to the uniformly integrable case. A similar method is used to prove Burkholder's martingale transform convergence theorem.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1973-0324770-X
Article copyright: © Copyright 1973 American Mathematical Society