A proof of the Burkholder theorem for martingale transforms
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- by T. Shintani PDF
- Proc. Amer. Math. Soc. 82 (1981), 278-279 Request permission
Abstract:
If $g$ is the transform of an ${L^1}$-bounded martingale $f$ under a predictable sequence $\upsilon$ satisfying ${\text {sup}_n}\left | {{\upsilon _n}} \right | < \infty$ almost everywhere, then a proof of the convergence of $g$ is given using an approximation of $f$ by a martingale of bounded variation.References
- D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37 (1966), 1494–1504. MR 208647, DOI 10.1214/aoms/1177699141
- D. L. Burkholder, A sharp inequality for martingale transforms, Ann. Probab. 7 (1979), no. 5, 858–863. MR 542135
- D. L. Burkholder and T. Shintani, Approximation of $L^{1}$-bounded martingales by martingales of bounded variation, Proc. Amer. Math. Soc. 72 (1978), no. 1, 166–169. MR 494472, DOI 10.1090/S0002-9939-1978-0494472-2
- Adriano M. Garsia, Martingale inequalities: Seminar notes on recent progress, Mathematics Lecture Note Series, W. A. Benjamin, Inc., Reading, Mass.-London-Amsterdam, 1973. MR 0448538
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 278-279
- MSC: Primary 60G42
- DOI: https://doi.org/10.1090/S0002-9939-1981-0609666-2
- MathSciNet review: 609666