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ArticleOriginal scientific text

Title

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

Authors 1, 2

Affiliations

  1. Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, CB#3260, Hanes Hall, Chapel Hill, NC 27599, USA
  2. Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston, MA 02215, USA

Abstract

Kernel functions of stable, self-similar mixed moving averages are known to be related to nonsingular flows. We identify and examine here a new functional occuring in this relation and study its properties. To prove its existence, we develop a general result about semi-additive functionals related to cocycles. The functional we identify, is helpful when solving for the kernel function generated by a flow. Its presence also sheds light on the previous results on the subject.

Keywords

ENG
stable, self-similar processes with stationary increments, mixed moving averages, nonsingular flows, cocycles, semi-additive functionals

Bibliography

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Discussiones Mathematicae Probability and Statistics
2010/30/2
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Pages:
149-177
Main language of publication
English
Received
2009-03-16
Published
2010

DOI: 10.7151/dmps.1126

Exact and natural sciences