A linear prediction problem for symmetric α-stable processes with 1/2<α<1

Yumiko SATO

doi:10.2969/jmsj/03910033

Yumiko SATO

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JOURNAL FREE ACCESS

1987 Volume 39 Issue 1 Pages 33-49

DOI https://doi.org/10.2969/jmsj/03910033

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Published: 1987 Received: June 28, 1985 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S. Cambanis and A. Soltami, Prediction of stable processes: spectral and moving average representations, Z. Wahr. Verw. Gel)., 66 (1984), 593-612.
2) O. Hanner, Deterministic and non-deterministic stationary stochastic processes, Ark. Mat., 1 (1949), 161-177.
3) T. Hida and N. Ikeda, Note on linear processes, J. Math. Kyoto Univ., 1 (1961), 75-86.
4) K. Karhunen, Über die Struktur stationärer zufällinger Funktionen, Ark. Mat., 1 (1949), 141-160.
5) P. Lévy, Fonctions aléatoires à corrélation linéaire, Illinois J. Math., 1 (1957), 217-258.
6) G. Maruyama, Infinitely divisible processes, Theory Probab. Appl., 15 (1970), 3-23.
7) Y. Sato, On Riemann type integral of functions with values in a certain Fréchet space, Proc. Japan Acad. Ser. A, 61 (1985), 249-251.
8) M. Schilder, Some structure theorems for the symmetric stable laws, Ann. Math. Statist., 41 (1970), 412-421.
9) K. Urbanik, Some prediction problems for strictly stationary processes, Proc. Fifth Berkeley Symp. on Math. Statist. and Probab. Val. II, Part 1, Univ. California Press, 1967, pp. 235-258.
10) K. Urbanik and W. A. Woyczynski, A random integral and Orlicz spaces, Bull. Acad. Polon. Sci., 15 (1967), 161-169.
11) A. Weron, Stable processes and measures; a survey, Probab. Theory on Vector Spaces III. Lublin, August 1983, Lecture Notes in Math., 1080, Springer, 1984.

Right : [1] S. Cambanis and A. Soltami, Prediction of stable processes: spectral and moving average representations, Z. Wahr. Verw. Geb., 66 (1984), 593-612.
[2] O. Hanner, Deterministic and non-deterministic stationary stochastic processes, Ark. Mat., 1 (1949), 161-177.
[3] T. Hida and N. Ikeda, Note on linear processes, J. Math. Kyoto Univ., 1 (1961), 75-86.
[4] K. Karhunen, Über die Struktur stationärer zufällinger Funktionen, Ark. Mat., 1 (1949), 141-160.
[5] P. Lévy, Fonctions aléatoires à corrélation linéaire, Illinois J. Math., 1 (1957), 217-258.
[6] G. Maruyama, Infinitely divisible processes, Theory Probab. Appl., 15 (1970), 3-23.
[7] Y. Sato, On Riemann type integral of functions with values in a certain Fréchet space, Proc. Japan Acad. Ser. A, 61 (1985), 249-251.
[8] M. Schilder, Some structure theorems for the symmetric stable laws, Ann. Math. Statist., 41 (1970), 412-421.
[9] K. Urbanik, Some prediction problems for strictly stationary processes, Proc. Fifth Berkeley Symp. on Math. Statist. and Probab. Vol. II, Part 1, Univ. California Press, 1967, pp. 235-258.
[10] K. Urbanik and W. A. Woyczynski, A random integral and Orlicz spaces, Bull. Acad. Polon. Sci., 15 (1967), 161-169.
[11] A. Weron, Stable processes and measures; a survey, Probab. Theory on Vector Spaces III. Lublin, August 1983, Lecture Notes in Math., 1080, Springer, 1984.

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