The complete convergence for partial sums of i.i.d. random variables. (English) Zbl 0554.60039

Bai, Zhidong; Su, Chun

Sci. Sin., Ser. A 28, 1261-1277 (1985).

In this paper by using the equivalence of the a.s. convergence and the convergence in probability for the partial sums of independent random variables, we improved and strengthened a series of M. Katz and L. E. Baum’s results [Trans. Am. Math. Soc. 120, 108-123 (1965; Zbl 0142.148)], which give some necessary and sufficient conditions about the complete convergence for the partial sums of iid random variables. On the above basis, we got ideal conditions and results about the complete convergence for the random selected partial sums of iid random variables.

MSC:

60F15	Strong limit theorems
60F05	Central limit and other weak theorems

Keywords:

convergence in probability; random selected partial sums

Citations:

Zbl 0142.148