Complete convergence of weighted sums of martingale differences. (English) Zbl 0698.60035

A sequence \(\{U_ n\), \(n\geq 1\}\) converges completely to the constant c if \[ \sum P(| U_ n-c| >\epsilon)<\infty \quad for\quad every\quad \epsilon >0. \] The now classical result of P. L. Hsu and H. Robbins [Proc. Nat. Acad. Sci. USA 33, 25-31 (1947; Zbl 0030.20101)] concerning complete convergence of the arithmetic mean of i.i.d. random variables has been generalized in various ways. The present paper deals with weighted sums of martingale differences.
Reviewer: A.Gut


60F15 Strong limit theorems
60G42 Martingales with discrete parameter


Zbl 0030.20101
Full Text: DOI


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