The convergence rate of some random series. (Russian) Zbl 0566.60032

Klesov, O. I.

Teor. Veroyatn. Mat. Stat. 30, 81-92 (1984).

Let \(\xi_ k\), \(k=1,2,..\). be random variables such that the series \(\sum \xi_ k\) converges almost surely. The problem considered is to find a sequence of numbers \(b_ n\) such that as \(b_ n\uparrow \infty\), \(b_ n\sum_{k\geq n}\xi_ k\to 0\) a.s. Starting with the general case the author successively considers various schemes of dependence of \(\xi_ n\) (independent, orthogonal, martingale etc.)

Reviewer: A.V.Nagaev

MSC:

60F15	Strong limit theorems
60G50	Sums of independent random variables; random walks
60G42	Martingales with discrete parameter

Keywords:

various schemes of dependence