A short proof of the martingale convergence theorem
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- by Charles W. Lamb PDF
- Proc. Amer. Math. Soc. 38 (1973), 215-217 Request permission
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
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- Luis Báez-Duarte, On the convergence of martingale transforms, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 19 (1971), 319–322. MR 300328, DOI 10.1007/BF00535836
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 215-217
- MSC: Primary 60G45
- DOI: https://doi.org/10.1090/S0002-9939-1973-0324770-X
- MathSciNet review: 0324770