Disjointness results for some classes of stable processes

• Autorzy: Michael Hernández , Christian Houdré
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42A45: Multipliers
• 60G99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 105
• Numer: 3
• Strony: 235-252

Daty

wydano

1993

otrzymano

1992-07-17

poprawiono

1993-02-15

Twórcy

autor

Michael Hernández

• Department of Mathematics, University of Maryland, College Park, Maryland 20742, U.S.A.

autor

Christian Houdré

• Department of Statistics, Stanford University, Stanford, California 94305, U.S.A.

Bibliografia

• [1] J. Benedetto and H. Heinig, Weighted Hardy spaces and the Laplace transform, in: Lecture Notes in Math. 992, Springer, 1983, 240-277.
• [2] S. Cambanis and C. Houdré, Stable processes: moving averages versus Fourier transforms, Probab. Theory Related Fields 95 (1993), 75-85.
• [3] S. Cambanis and R. Soltani, Prediction of stable processes: spectral and moving average representations, Z. Warhrsch. Verw. Gebiete 66 (1984), 593-612.
• [4] N. Dunford and J. Schwartz, Linear Operators, Part I: General Theory, Wiley Interscience, New York 1957.
• [5] R. Edwards and G. Gaudry, Littlewood-Paley and Multiplier Theory, Springer, Berlin 1977.
• [6] C. Houdré, Harmonizability, V-boundedness, (2,p)-boundedness of stochastic processes, Probab. Theory Related Fields 84 (1990), 39-54.
• [7] C. Houdré, Linear and Fourier stochastic analysis, ibid. 87 (1990), 167-188.
• [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] W. Jurkat and G. Sampson, On rearrangement and weight inequalities for the Fourier transform, Indiana Univ. Math. J. 33 (1984), 257-270.
• [10] J. Lakey, Weighted norm inequalities for the Fourier transform, Ph.D. Thesis, University of Maryland, College Park, 1991.
• [11] A. Makagon and V. Mandrekar, The spectral representation of stable processes: harmonizability and regularity, Probab. Theory Related Fields 85 (1990), 1-11.
• [12] B. Rajput and J. Rosinski, Spectral representations of infinitely divisible processes, ibid. 82 (1989), 451-487.
• [13] J. Rosinski, On stochastic integral representation of stable processes with sample paths in Banach spaces, J. Multivariate Anal. 20 (1986), 277-307.
• [14] G. Samorodnitsky and M. Taqqu, Stable Random Processes, book to appear.
• [15] K. Urbanik, Prediction of strictly stationary sequences, Colloq. Math. 12 (1964), 115-129.
• [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.
• [17] K. Urbanik, Random measures and harmonizable sequences, Studia Math. 31 (1968), 61-88.