Chaotic behavior of infinitely divisible processes

S. Cambanis; K. Podgórski; A. Weron

Studia Mathematica (1995)

  • Volume: 115, Issue: 2, page 109-127
  • ISSN: 0039-3223

Abstract

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The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.

How to cite

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Cambanis, S., Podgórski, K., and Weron, A.. "Chaotic behavior of infinitely divisible processes." Studia Mathematica 115.2 (1995): 109-127. <http://eudml.org/doc/216202>.

@article{Cambanis1995,
abstract = {The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.},
author = {Cambanis, S., Podgórski, K., Weron, A.},
journal = {Studia Mathematica},
keywords = {infinitely divisible process; ergodicity and mixing; stationary process; stochastic representation; Musielak-Orlicz space; hierarchy of chaos; infinitely divisible processes; stationary processes},
language = {eng},
number = {2},
pages = {109-127},
title = {Chaotic behavior of infinitely divisible processes},
url = {http://eudml.org/doc/216202},
volume = {115},
year = {1995},
}

TY - JOUR
AU - Cambanis, S.
AU - Podgórski, K.
AU - Weron, A.
TI - Chaotic behavior of infinitely divisible processes
JO - Studia Mathematica
PY - 1995
VL - 115
IS - 2
SP - 109
EP - 127
AB - The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.
LA - eng
KW - infinitely divisible process; ergodicity and mixing; stationary process; stochastic representation; Musielak-Orlicz space; hierarchy of chaos; infinitely divisible processes; stationary processes
UR - http://eudml.org/doc/216202
ER -

References

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  4. S. Cambanis and A. Ławniczak (1989), Ergodicity and mixing of infinitely divisible processes, unpublished preprint. 
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  16. J. Musielak (1983), Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer, New York. D. Newton (1968), On a principal factor system of a normal dynamical system, J. London Math. Soc. 43, 275-279. Zbl0169.20601
  17. K. Podgórski (1992), A note on ergodic symmetric stable processes, Stochastic Process. Appl. 43, 355-362. Zbl0758.60036
  18. K. Podgórski and A. Weron (1991), Characterization of ergodic stable processes via the dynamical functional, in: Stable Processes and Related Topics, S. Cambanis et al. (eds.), Birkhäuser, Boston, 317-328. Zbl0723.60034
  19. B. S. Rajput and J. Rosiński (1989), Spectral representations of infinitely divisible processes, Probab. Theory Related Fields 82, 451-487. Zbl0659.60078
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  22. A. Weron (1985), Harmonizable stable processes on groups: spectral, ergodic and interpolation properties, Z. Wahrsch. Verw. Gebiete 68, 473-491. Zbl0537.60008

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