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## Discussiones Mathematicae Probability and Statistics

2010 | 30 | 2 | 149-177
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
149-177
Opis fizyczny
Daty
wydano
2010
otrzymano
2009-03-16
Twórcy
autor
• Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, CB#3260, Hanes Hall, Chapel Hill, NC 27599, USA
autor
• Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston, MA 02215, USA
Bibliografia
• [1] N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular Variation, Cambridge University Press 1987.
• [2] I.P. Cornfeld, S.V. Fomin and Y.G. Sinai, Ergodic Theory, Springer-Verlag 1982.
• [3] C.D. Jr. Hardin, Isometries on subspaces of $L^p$, Indiana University Mathematics Journal 30 (1981), 449-465.
• [4] S. Kolodyński and J. Rosiński, Group self-similar stable processes in $ℝ^d$, Journal of Theoretical Probability 16 (4) (2002), 855-876.
• [5] I. Kubo, Quasi-flows, Nagoya Mathematical Journal 35 (1969), 1-30.
• [6] I. Kubo, Quasi-flows II: Additive functionals and TQ-systems, Nagoya Mathematical Journal 40 (1970), 39-66.
• [7] V. Pipiras and M.S. Taqqu, Decomposition of self-similar stable mixed moving averages, Probability Theory and Related Fields 123 (3)(2002 a), 412-452.
• [8] V. Pipiras and M.S. Taqqu, The structure of self-similar stable mixed moving averages, The Annals of Probability 30 (2) (2002 b), 898-932.
• [9] V. Pipiras and M.S. Taqqu, Stable stationary processes related to cyclic flows, The Annals of Probability 32 (3A) (2004), 2222-2260.
• [10] Preprint. Available at http://www.stat.unc.edu/faculty/pipiras/preprints/articles.html.
• [11] J. Rosiński, On the structure of stationary stable processes, The Annals of Probability 23 (1995), 1163-1187.
• [12] R.J. Zimmer, Ergodic Theory and Semisimple Groups, Birkhäuser, Boston 1984.
Typ dokumentu
Bibliografia
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