Spectral density estimation for stationary stable random fields

Rachid Sabre

Applicationes Mathematicae (1995)

  • Volume: 23, Issue: 2, page 107-133
  • ISSN: 1233-7234

Abstract

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We consider a stationary symmetric stable bidimensional process with discrete time, having the spectral representation (1.1). We consider a general case where the spectral measure is assumed to be the sum of an absolutely continuous measure, a discrete measure of finite order and a finite number of absolutely continuous measures on several lines. We estimate the density of the absolutely continuous measure and the density on the lines.

How to cite

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Sabre, Rachid. "Spectral density estimation for stationary stable random fields." Applicationes Mathematicae 23.2 (1995): 107-133. <http://eudml.org/doc/219120>.

@article{Sabre1995,
abstract = {We consider a stationary symmetric stable bidimensional process with discrete time, having the spectral representation (1.1). We consider a general case where the spectral measure is assumed to be the sum of an absolutely continuous measure, a discrete measure of finite order and a finite number of absolutely continuous measures on several lines. We estimate the density of the absolutely continuous measure and the density on the lines.},
author = {Sabre, Rachid},
journal = {Applicationes Mathematicae},
keywords = {(S.α.S) process; double kernel method; periodogram; Jackson kernel; stationary symmetric stable bidimensional process; discrete time},
language = {eng},
number = {2},
pages = {107-133},
title = {Spectral density estimation for stationary stable random fields},
url = {http://eudml.org/doc/219120},
volume = {23},
year = {1995},
}

TY - JOUR
AU - Sabre, Rachid
TI - Spectral density estimation for stationary stable random fields
JO - Applicationes Mathematicae
PY - 1995
VL - 23
IS - 2
SP - 107
EP - 133
AB - We consider a stationary symmetric stable bidimensional process with discrete time, having the spectral representation (1.1). We consider a general case where the spectral measure is assumed to be the sum of an absolutely continuous measure, a discrete measure of finite order and a finite number of absolutely continuous measures on several lines. We estimate the density of the absolutely continuous measure and the density on the lines.
LA - eng
KW - (S.α.S) process; double kernel method; periodogram; Jackson kernel; stationary symmetric stable bidimensional process; discrete time
UR - http://eudml.org/doc/219120
ER -

References

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  3. [3] S. Cambanis, Complex symmetric stable variables and processes, in: P. K. Sen (ed.), Contributions to Statistics: Essays in Honour of Norman L. Johnson, North-Holland, New York, 1982, 63-79. 
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  9. [9] L. Heinrich, On the convergence of U-statistics with stable limit distribution, J. Multivariate Anal. 44 (1993), 266-278. Zbl0768.60023
  10. [10] Y. Hosoya, Discrete-time stable processes and their certain properties, Ann. Probab. 6 (1978), 94-105. Zbl0374.60045
  11. [11] E. Masry and S. Cambanis, Spectral density estimation for stationary stable processes, Stochastic Process. Appl. 18 (1984), 1-31. Zbl0541.62076
  12. [12] M. B. Priestley, Spectral Analysis and Time Series, Probab. Math. Statist., Academic Press, 1981. Zbl0537.62075
  13. [13] R. Sabre, Estimation non paramétrique dans les processus symétriques stables, Thèse de doctorat en Mathématiques, Université de Rouen, 1993. 
  14. [14] M. Schilder, Some structure theorems for the symmetric stable laws, Ann. Math. Statist. 42 (1970), 412-421. Zbl0196.19401
  15. [15] R. Song, Probabilistic approach to the Dirichlet problem of perturbed stable processes, Probab. Theory Related Fields 95 (1993), 371-389. Zbl0792.60067

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