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September 2005 Null flows, positive flows and the structure of stationary symmetric stable processes
Gennady Samorodnitsky
Ann. Probab. 33(5): 1782-1803 (September 2005). DOI: 10.1214/009117905000000305

Abstract

This paper elucidates the connection between stationary symmetric α-stable processes with 0<α<2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those corresponding to positive flows and those corresponding to null flows. We show that necessary and sufficient for a stationary stable process to be ergodic is that its positive component vanishes.

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Gennady Samorodnitsky. "Null flows, positive flows and the structure of stationary symmetric stable processes." Ann. Probab. 33 (5) 1782 - 1803, September 2005. https://doi.org/10.1214/009117905000000305

Information

Published: September 2005
First available in Project Euclid: 22 September 2005

zbMATH: 1080.60033
MathSciNet: MR2165579
Digital Object Identifier: 10.1214/009117905000000305

Subjects:
Primary: 60G10 , 60G52
Secondary: 37A40

Keywords: conservative flow , dissipative flow , ergodic theory , ergodicity , integral representation , nonsingular flow , null flow , positive flow , Stable process , stationary process

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 5 • September 2005
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