## The Annals of Probability

- Ann. Probab.
- Volume 40, Number 3 (2012), 1357-1374.

### Maharam extension and stationary stable processes

#### Abstract

We give a second look at stationary stable processes by interpreting the self-similar property at the level of the Lévy measure as characteristic of a Maharam system. This allows us to derive structural results and their ergodic consequences.

#### Article information

**Source**

Ann. Probab., Volume 40, Number 3 (2012), 1357-1374.

**Dates**

First available in Project Euclid: 4 May 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1336136066

**Digital Object Identifier**

doi:10.1214/11-AOP671

**Mathematical Reviews number (MathSciNet)**

MR2962094

**Zentralblatt MATH identifier**

1255.60077

**Subjects**

Primary: 60G52: Stable processes 60G10: Stationary processes 37A40: Nonsingular (and infinite-measure preserving) transformations

Secondary: 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10]

**Keywords**

Stable stationary processes Maharam system ergodic properties

#### Citation

Roy, Emmanuel. Maharam extension and stationary stable processes. Ann. Probab. 40 (2012), no. 3, 1357--1374. doi:10.1214/11-AOP671. https://projecteuclid.org/euclid.aop/1336136066