LIMIT THEOREMS FOR PRODUCTS OF SUMS OF INDEPENDENT
RANDOM VARIABLES
Tomasz K. Krajka
Zdzisław Rychlik
Abstract: Let be a sequence of independent random variables with finite second
moments and be a sequence of positive integer-valued random variables.
Write and let be a standard normal random variable. In
the paper the convergences
are
considered for some sequences
and
of positive integer numbers such that
a.e. The case when
are random variables is also considered. The main
results generalize the main theorems presented by Pang et al. [3].
2000 AMS Mathematics Subject Classification: Primary: 60F05; Secondary:
60G50.
Keywords and phrases: Lognormal distribution; randomly indexed product of sums;
central limit theorem; self-normalized.