Null flows, positive flows and the structure of stationary symmetric stable processes
Gennady Samorodnitsky
Source: Ann. Probab. Volume 33, Number 5
(2005), 1782-1803.
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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Keywords: Stable process; stationary process; integral representation; ergodic theory; nonsingular flow; dissipative flow; conservative flow; null flow; positive flow; ergodicity
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Permanent link to this document: http://projecteuclid.org/euclid.aop/1127395873
Digital Object Identifier: doi:10.1214/009117905000000305
Mathematical Reviews number (MathSciNet): MR2165579
Zentralblatt MATH identifier: 1080.60033
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