Null flows, positive flows and the structure of stationary symmetric stable processes
Null flows, positive flows and the structure of stationary symmetric stable processes
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零流、正流和平稳对称稳定过程的结构
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
G. Samorodnitsky
中科院分区：
文献类型：
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作者：
G. Samorodnitsky
本文通过描述平稳对称α-稳定过程的一种新的、唯一的分解，将平稳对称α-稳定过程分解为对应于正流和对应于零流的过程，从而阐明了0 < α < 2的平稳对称α-稳定过程与测度空间上的非奇异流之间的联系.证明了平稳过程遍历的充要条件是其正分量为零。
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.