Limit behavior of sums of a multiplicative system. (English. Russian original) Zbl 0626.60043

Matsak, I. K.

Theory Probab. Math. Stat. 33, 87-89 (1986); translation from Teor. Veroyatn. Mat. Stat. 33, 79-81 (1985).

The author studies the asymptotic behaviour of sums of certain products of coin-tossing variables as follows:
Let \(\{\xi_ p\}\), where p is a prime number, be independent coin- tossing variables and define \(\xi_ n=\xi_ a\cdot \xi_ b\) if \(n=ab\) and set \(S_ n=\sum^{n}_{k=1}\xi_ k\), \(k\geq 1\), \((\xi_ 1=1)\). Estimates for the magnitude of \(| S_ n|\) are obtained.

Reviewer: A.Gut

MSC:

60G50	Sums of independent random variables; random walks
42C10	Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
60G15	Gaussian processes

Keywords:

asymptotic behaviour; products of coin-tossing variables