自相似背景下的半可加泛函与上循环
Semi-additive functionals and cocycles in the context of self-similarity
摘要：
自相似对称$α$ -稳定、$α\in(0,2)$、混合移动平均线可以与非奇异流相关。通过使用这种关系和底层流的结构，可以将自相似混合移动平均线分解为不同的类，然后分别检查每个类中的过程。过程和流之间的关系涉及半加性泛函。我们建立了一个关于上循环的半可加泛函的一般性结果，并证明了过程与流之间的关系中存在一个新的半可加泛函。这个新的泛函对于寻找由给定流产生的自相似混合移动平均线的核函数是有用的。它也揭示了新的光在这个问题上以前的结果。
英文摘要：
Self-similar symmetric $α$-stable, $α\in(0,2)$, mixed moving averages can be related to nonsingular flows. By using this relation and the structure of the underlying flows, one can decompose self-similar mixed moving averages into distinct classes and then examine the processes in each of these classes separately. The relation between processes and flows involves semi-additive functionals. We establish a general result about semi-additive functionals related to cocycles, and identify the presence of a new semi-additive functional in the relation between processes and flows. This new functional is useful for finding the kernel function of self-similar mixed moving averages generated by a given flow. It also sheds new light on previous results on the subject.
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