## The Annals of Probability

- Ann. Probab.
- Volume 3, Number 2 (1975), 281-288.

### The Law of Large Numbers for Subsequences of a Stationary Process

Julius Blum and Bennett Eisenberg

#### Abstract

Convergence in mean of $N^{-1} \sum^N_{k=1} X_{t_k}$ is studied for stationary processes classified according to parameter space and type of spectral measure.

#### Article information

**Source**

Ann. Probab., Volume 3, Number 2 (1975), 281-288.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176996398

**Digital Object Identifier**

doi:10.1214/aop/1176996398

**Mathematical Reviews number (MathSciNet)**

MR370718

**Zentralblatt MATH identifier**

0309.60025

**JSTOR**

links.jstor.org

**Subjects**

Primary: 28A65

Secondary: 60610 62M99: None of the above, but in this section

**Keywords**

Estimation of the mean spectral measure ergodic theorem weak convergence to Haar measure

#### Citation

Blum, Julius; Eisenberg, Bennett. The Law of Large Numbers for Subsequences of a Stationary Process. Ann. Probab. 3 (1975), no. 2, 281--288. doi:10.1214/aop/1176996398. https://projecteuclid.org/euclid.aop/1176996398