Sums of independent random variables and the Burkholder transforms

Gabriel, J.-P.

doi:10.1090/S0002-9939-1977-0451392-6

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
DOI: https://doi.org/10.1090/S0002-9939-1977-0451392-6
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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