## Bernoulli

• Bernoulli
• Volume 9, Number 6 (2003), 985-1002.

### Baum--Katz laws for certain weighted sums of independent and identically distributed random variables

#### Abstract

We consider weighted sums $\sum_k p_{nk}\, X_k$ of independent and identically distributed random variables $(X_n)$ and compare the tail probabilities of these sums with the moment conditions on $X_1$, that is, we prove various results of Baum--Katz type. Some special examples of weights $p_{nk}$ originating from summability are discussed.

#### Article information

Source
Bernoulli, Volume 9, Number 6 (2003), 985-1002.

Dates
First available in Project Euclid: 23 December 2003

https://projecteuclid.org/euclid.bj/1072215198

Digital Object Identifier
doi:10.3150/bj/1072215198

Mathematical Reviews number (MathSciNet)
MR2046815

Zentralblatt MATH identifier
1047.60045

#### Citation

Lanzinger, Hartmut; Stadtmüller, Ulrich. Baum--Katz laws for certain weighted sums of independent and identically distributed random variables. Bernoulli 9 (2003), no. 6, 985--1002. doi:10.3150/bj/1072215198. https://projecteuclid.org/euclid.bj/1072215198