Disjointness results for some classes of stable processes

Michael Hernández; Christian Houdré

Studia Mathematica (1993)

  • Volume: 105, Issue: 3, page 235-252
  • ISSN: 0039-3223

Abstract

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We discuss the disjointness of two classes of stable stochastic processes: moving averages and Fourier transforms. Results on the incompatibility of these two representations date back to Urbanik. Here we extend various disjointness results to encompass larger classes of processes.

How to cite

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Hernández, Michael, and Houdré, Christian. "Disjointness results for some classes of stable processes." Studia Mathematica 105.3 (1993): 235-252. <http://eudml.org/doc/215996>.

@article{Hernández1993,
abstract = {We discuss the disjointness of two classes of stable stochastic processes: moving averages and Fourier transforms. Results on the incompatibility of these two representations date back to Urbanik. Here we extend various disjointness results to encompass larger classes of processes.},
author = {Hernández, Michael, Houdré, Christian},
journal = {Studia Mathematica},
keywords = {stable stochastic processes; Fourier transforms},
language = {eng},
number = {3},
pages = {235-252},
title = {Disjointness results for some classes of stable processes},
url = {http://eudml.org/doc/215996},
volume = {105},
year = {1993},
}

TY - JOUR
AU - Hernández, Michael
AU - Houdré, Christian
TI - Disjointness results for some classes of stable processes
JO - Studia Mathematica
PY - 1993
VL - 105
IS - 3
SP - 235
EP - 252
AB - We discuss the disjointness of two classes of stable stochastic processes: moving averages and Fourier transforms. Results on the incompatibility of these two representations date back to Urbanik. Here we extend various disjointness results to encompass larger classes of processes.
LA - eng
KW - stable stochastic processes; Fourier transforms
UR - http://eudml.org/doc/215996
ER -

References

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  1. [1] J. Benedetto and H. Heinig, Weighted Hardy spaces and the Laplace transform, in: Lecture Notes in Math. 992, Springer, 1983, 240-277. 
  2. [2] S. Cambanis and C. Houdré, Stable processes: moving averages versus Fourier transforms, Probab. Theory Related Fields 95 (1993), 75-85. Zbl0794.60027
  3. [3] S. Cambanis and R. Soltani, Prediction of stable processes: spectral and moving average representations, Z. Warhrsch. Verw. Gebiete 66 (1984), 593-612. Zbl0528.60035
  4. [4] N. Dunford and J. Schwartz, Linear Operators, Part I: General Theory, Wiley Interscience, New York 1957. Zbl0084.10402
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  7. [7] C. Houdré, Linear and Fourier stochastic analysis, ibid. 87 (1990), 167-188. Zbl0688.60028
  8. [8] R. Johnson, Recent results on weighted inequalities for the Fourier transform, in: Seminar Analysis of the Karl-Weierstraß-Institute 1986/87, Teubner-Texte Math. 106, B. Schulze and H. Triebel (eds.), Teubner, Leipzig 1988, 287-296. 
  9. [9] W. Jurkat and G. Sampson, On rearrangement and weight inequalities for the Fourier transform, Indiana Univ. Math. J. 33 (1984), 257-270. Zbl0536.42013
  10. [10] J. Lakey, Weighted norm inequalities for the Fourier transform, Ph.D. Thesis, University of Maryland, College Park, 1991. 
  11. [11] A. Makagon and V. Mandrekar, The spectral representation of stable processes: harmonizability and regularity, Probab. Theory Related Fields 85 (1990), 1-11. Zbl0673.60041
  12. [12] B. Rajput and J. Rosinski, Spectral representations of infinitely divisible processes, ibid. 82 (1989), 451-487. Zbl0659.60078
  13. [13] J. Rosinski, On stochastic integral representation of stable processes with sample paths in Banach spaces, J. Multivariate Anal. 20 (1986), 277-307. Zbl0606.60041
  14. [14] G. Samorodnitsky and M. Taqqu, Stable Random Processes, book to appear. 
  15. [15] K. Urbanik, Prediction of strictly stationary sequences, Colloq. Math. 12 (1964), 115-129. Zbl0126.33502
  16. [16] K. Urbanik, Some prediction problems for strictly stationary processes, in: Proc. 5th Berkeley Sympos. Math. Statist. Probab., Vol. 2, Part I, Univ. of California Press, 1967, 235-258. Zbl0226.60065
  17. [17] K. Urbanik, Random measures and harmonizable sequences, Studia Math. 31 (1968), 61-88. Zbl0249.60014

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