English

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

Probability 2007-05-23 v1

Abstract

Self-similar symmetric α\alpha-stable, α(0,2)\alpha\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.

Keywords

Cite

@article{arxiv.math/0405067,
  title  = {Semi-additive functionals and cocycles in the context of self-similarity},
  author = {Vladas Pipiras and Murad S. Taqqu},
  journal= {arXiv preprint arXiv:math/0405067},
  year   = {2007}
}