## The Annals of Probability

- Ann. Probab.
- Volume 16, Number 1 (1988), 313-332.

### A Central Limit Theorem for Stationary $\rho$-Mixing Sequences with Infinite Variance

#### Abstract

A central limit theorem is proved for some strictly stationary $\rho$-mixing sequences with infinite second moments. The condition on the tails of the marginal distribution is the same as in the corresponding classic result for i.i.d. sequences. The mixing rate is essentially the slowest possible for this result.

#### Article information

**Source**

Ann. Probab., Volume 16, Number 1 (1988), 313-332.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176991904

**Digital Object Identifier**

doi:10.1214/aop/1176991904

**Mathematical Reviews number (MathSciNet)**

MR920274

**Zentralblatt MATH identifier**

0643.60018

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F05: Central limit and other weak theorems

Secondary: 60G10: Stationary processes

**Keywords**

Strictly stationary $\rho$-mixing infinite variance central limit theorem

#### Citation

Bradley, Richard C. A Central Limit Theorem for Stationary $\rho$-Mixing Sequences with Infinite Variance. Ann. Probab. 16 (1988), no. 1, 313--332. doi:10.1214/aop/1176991904. https://projecteuclid.org/euclid.aop/1176991904