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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Sums of independent random variables and the Burkholder transforms


Author: J.-P. Gabriel
Journal: Proc. Amer. Math. Soc. 66 (1977), 123-127
MSC: Primary 60G45; Secondary 60G50
MathSciNet review: 0451392
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Abstract: This note shows a connection between the unconditionally a.e. convergence of series with independent increments and the a.e. convergence of their Burkholder transforms. Using this result, it is then proved that the $ {L_1}$-bounded condition of Burkholder is the best one in the class of martingales, which assures the a.e. convergence of their transforms.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0451392-6
PII: S 0002-9939(1977)0451392-6
Keywords: Independent random variables, unconditionally a.e. convergence, Burkholder transform, martingales
Article copyright: © Copyright 1977 American Mathematical Society