## The Annals of Probability

- Ann. Probab.
- Volume 13, Number 4 (1985), 1279-1285.

### An Improved Subadditive Ergodic Theorem

#### Abstract

A new version of Kingman's subadditive ergodic theorem is presented, in which the subadditivity and stationarity assumptions are relaxed without weakening the conclusions. This result applies to a number of situations that were not covered by Kingman's original theorem. The proof involves a rather simple reduction to the additive case, where Birkhoff's ergodic theorem can be applied.

#### Article information

**Source**

Ann. Probab., Volume 13, Number 4 (1985), 1279-1285.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176992811

**Digital Object Identifier**

doi:10.1214/aop/1176992811

**Mathematical Reviews number (MathSciNet)**

MR806224

**Zentralblatt MATH identifier**

0579.60023

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F15: Strong theorems

Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

**Keywords**

Subadditive processes ergodic theory percolation contact processes

#### Citation

Liggett, Thomas M. An Improved Subadditive Ergodic Theorem. Ann. Probab. 13 (1985), no. 4, 1279--1285. doi:10.1214/aop/1176992811. https://projecteuclid.org/euclid.aop/1176992811