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

Vladas Pipiras; Murad S. Taqqu

Discussiones Mathematicae Probability and Statistics (2010)

  • Volume: 30, Issue: 2, page 149-177
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Vladas Pipiras, and Murad S. Taqqu. "Semi-additive functionals and cocycles in the context of self-similarity." Discussiones Mathematicae Probability and Statistics 30.2 (2010): 149-177. <http://eudml.org/doc/277078>.

@article{VladasPipiras2010,
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.},
author = {Vladas Pipiras, Murad S. Taqqu},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {stable; self-similar processes with stationary increments; mixed moving averages; nonsingular flows; cocycles; semi-additive functionals; self-similar process with stationary increments},
language = {eng},
number = {2},
pages = {149-177},
title = {Semi-additive functionals and cocycles in the context of self-similarity},
url = {http://eudml.org/doc/277078},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Vladas Pipiras
AU - Murad S. Taqqu
TI - Semi-additive functionals and cocycles in the context of self-similarity
JO - Discussiones Mathematicae Probability and Statistics
PY - 2010
VL - 30
IS - 2
SP - 149
EP - 177
AB - 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.
LA - eng
KW - stable; self-similar processes with stationary increments; mixed moving averages; nonsingular flows; cocycles; semi-additive functionals; self-similar process with stationary increments
UR - http://eudml.org/doc/277078
ER -

References

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  7. [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. Zbl1007.60026
  8. [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. Zbl1016.60057
  9. [9] V. Pipiras and M.S. Taqqu, Stable stationary processes related to cyclic flows, The Annals of Probability 32 (3A) (2004), 2222-2260. Zbl1054.60056
  10. [10] Preprint. Available at http://www.stat.unc.edu/faculty/pipiras/preprints/articles.html. 
  11. [11] J. Rosiński, On the structure of stationary stable processes, The Annals of Probability 23 (1995), 1163-1187. Zbl0836.60038
  12. [12] R.J. Zimmer, Ergodic Theory and Semisimple Groups, Birkhäuser, Boston 1984. Zbl0571.58015

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