On the rate of convergence of series of random variables. (English. Ukrainian original) Zbl 0941.60043

Num, E.; Rosalskyj, A.

Theory Probab. Math. Stat. 52, 129-140 (1996); translation from Teor. Jmovirn. Mat. Stat. 52, 120-131 (1995).

Let the series of random variables \(\sum_{j=1}^{\infty}X_j\) converge almost surely. Let \(T_n=\sum_{j=n}^{\infty}X_j.\) Conditions for convergence of \(\sup_{k \geq n} |T_k|/b_n\) to \(0\) in probability are stated. The weighted series of identically distributed random variables are analysed. New problems are formulated.

Reviewer: A.Ya.Olenko (Kyïv)

MSC:

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

Keywords:

series of random variables; speed of convergence