Geodesic
Semi-additive functionals and cocycles in the context of self-similarity
Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 2, pp. 149-177.

Voir la notice de l'article provenant de la source Library of Science

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: stable, self-similar processes with stationary increments, mixed moving averages, nonsingular flows, cocycles, semi-additive functionals 
@article{DMPS_2010_30_2_a0,
     author = {Pipiras, Vladas and Taqqu, Murad},
     title = {Semi-additive functionals and cocycles in the context of self-similarity},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {149--177},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2010},
     zbl = {1235.60035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMPS_2010_30_2_a0/}
}
TY  - JOUR
AU  - Pipiras, Vladas
AU  - Taqqu, Murad
TI  - Semi-additive functionals and cocycles in the context of self-similarity
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2010
SP  - 149
EP  - 177
VL  - 30
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMPS_2010_30_2_a0/
LA  - en
ID  - DMPS_2010_30_2_a0
ER  - 
%0 Journal Article
%A Pipiras, Vladas
%A Taqqu, Murad
%T Semi-additive functionals and cocycles in the context of self-similarity
%J Discussiones Mathematicae. Probability and Statistics
%D 2010
%P 149-177
%V 30
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMPS_2010_30_2_a0/
%G en
%F DMPS_2010_30_2_a0
Pipiras, Vladas; Taqqu, Murad. Semi-additive functionals and cocycles in the context of self-similarity. Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 2, pp. 149-177. http://geodesic.mathdoc.fr/item/DMPS_2010_30_2_a0/

[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.