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Semi-additive functionals and cocycles in the context of self-similarity

Vladas Pipiras·Murad S. Taqqu
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Abstract

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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Vladas Pipiras, Murad S. Taqqu. 2004-05-04. Semi-additive functionals and cocycles in the context of self-similarity. https://arxiv.org/abs/math/0405067

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