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Stochastic processes as Fourier integrals and dilation of vector measures
Author(s):
Christian
Houdré
Journal:
Bull. Amer. Math. Soc.
21
(1989),
281-285.
MSC (1985):
Primary 60G12;
Secondary 46G10
MathSciNet review:
998198
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References:
- [B] S. Bochner, Stationarity, boundedness, almost periodicity of random valued functions, Proc. Third Berkeley Sympos. Math. Statist. Prob. 2 (1956), 7-27. MR 84883
- [C] H. Cramér, On harmonic analysis in certain functional spaces, Ark. Mat. Astr. Fys. 28B (1942), 7 pp. MR 6609
- [D] N. Dinculeanu, Vector measures, Pergamon Press, Oxford, 1967. MR 206190
- [GV] I. M. Gel'fand and N. Vilenkin, Generalized functions, Vol. 4, Applications of Harmonic Analysis, Academic Press, New York, 1964. MR 173945
- [Hi] T. Hida, Brownian motion, Applications of Mathematics, vol. 11, Springer-Verlag, Berlin and New York, 1980. MR 562914
- [Ho1] C. Houdré, Harmonizability, V-boundedness, (2, P)-boundedness of stochastic processes, Center for Stochastic Processes Tech. Rept. no. 239, Univ. of North Carolina, 1988, Prob. Theory and Rel. Fields (to appear). MR 1027819
- [Ho2] C. Houdré, Linear Fourier and stochastic analysis, Center for Stochastic Processes Tech. Rept. no. 258, University of North Carolina, 1989. MR 1080488
- [K] I. Kluvánek, Characterization of Fourier-Stieltjes transformations of vector and operator valued measures, Czech. Math. J. 17 (1967), 261-277. MR 230872
- [N] H. Niemi, On orthogonality scattered dilations of bounded vector measures, Ann. Acad. Sci. Fenn. AI Math. 3 (1977), 43-52. MR 632060
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- [Pi] G. Pisier, Factorization of linear operators and geometry of Banach spaces, CBMS Regional Conf. Ser. in Math. no. 60, Amer. Math. Soc., Providence, R.I., 1986. MR 829919
- [S] E. Slutsky, Sur les fonctions aléatoires presque périodiques et sur la décomposition des fonctions aléatoires stationnaires en composantes, Actualités. Sci. Ind. no. 738 (1938), 35-55, Hermann & Cie, Paris.
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Additional Information:
DOI:
10.1090/S0273-0979-1989-15830-8
PII:
S 0273-0979(1989)15830-8
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