## Bernoulli

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

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

Hartmut Lanzinger and Ulrich Stadtmüller

#### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.3150/bj/1072215198

**Mathematical Reviews number (MathSciNet)**

MR2046815

**Zentralblatt MATH identifier**

1047.60045

**Keywords**

Baum-Katz laws tail probabilities weighted mean

#### 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