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Null flows, positive flows and the structure of stationary symmetric stable processes

Gennady Samorodnitsky
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Abstract

This paper elucidates the connection between stationary symmetric alpha-stable processes with 0<alpha<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 a necessary and sufficient for a stationary stable process to be ergodic is that its positive component vanishes.

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Gennady Samorodnitsky. 2004-12-21. Null flows, positive flows and the structure of stationary symmetric stable processes. https://arxiv.org/abs/math/0412419

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