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1995-1996 | 23 | 2 | 107-133
Tytuł artykułu

Spectral density estimation for stationary stable random fields

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
23
Numer
2
Strony
107-133
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-10-22
poprawiono
1994-07-05
Twórcy
autor
  • Etablissement National D'Enseignement Supérieur, Agronomique de Dijon, 26, Boulevard du Dr. Petitjean, B.P. 1607, F-21036 Dijon, France
Bibliografia
  • [1] B. S. Rajput and J. Rosinski, Spectral representations of infinitely divisible processes, Probab. Theory Related Fields 82 (1989), 451-487.
  • [2] M. Bertrand-Retali, Processus symétriques α-stables, Séminaire de Probabilité et Statistique à l'Université de Constantine, Algérie, 1987.
  • [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.
  • [4] S. Cambanis and G. Miller, Some path properties of pth order and symmetric stable processes, Ann. Probab. 8 (1980), 1148-1156.
  • [5] S. Cambanis and G. Miller, Linear problems in pth order and stable processes, SIAM J. Appl. Math. 41 (1981), 43-69.
  • [6] N. Demesh, Application of the polynomial kernels to the estimation of the spectra of discrete stable stationary processes, Akad. Nauk Ukrain. SSR, Inst. Mat. Preprint 64 (1988), 12-36 (in Russian).
  • [7] V. K. Dzyadyk, Introduction à la théorie de l'approximation uniforme par fonctions polynomiales, Nauka, 1977 (in Russian).
  • [8] C. D. Hardin, On the spectral representation theorem for symmetric stable processes, J. Multivariate Anal. 12 (1982), 385-401.
  • [9] L. Heinrich, On the convergence of U-statistics with stable limit distribution, J. Multivariate Anal. 44 (1993), 266-278.
  • [10] Y. Hosoya, Discrete-time stable processes and their certain properties, Ann. Probab. 6 (1978), 94-105.
  • [11] E. Masry and S. Cambanis, Spectral density estimation for stationary stable processes, Stochastic Process. Appl. 18 (1984), 1-31.
  • [12] M. B. Priestley, Spectral Analysis and Time Series, Probab. Math. Statist., Academic Press, 1981.
  • [13] R. Sabre, Estimation non paramétrique dans les processus symétriques stables, Thèse de doctorat en Mathématiques, Université de Rouen, 1993.
  • [14] M. Schilder, Some structure theorems for the symmetric stable laws, Ann. Math. Statist. 42 (1970), 412-421.
  • [15] R. Song, Probabilistic approach to the Dirichlet problem of perturbed stable processes, Probab. Theory Related Fields 95 (1993), 371-389.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv23i2p107bwm
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