The Annals of Probability

Maharam extension and stationary stable processes

Emmanuel Roy

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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

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

First available in Project Euclid: 4 May 2012

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Zentralblatt MATH identifier

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]

Stable stationary processes Maharam system ergodic properties


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

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