Stochastic processes as Fourier integrals and dilation of vector measures
Author:
Christian Houdré
Journal:
Bull. Amer. Math. Soc. 21 (1989), 281-285
MSC (1985):
Primary 60G12; Secondary 46G10
DOI:
https://doi.org/10.1090/S0273-0979-1989-15830-8
MathSciNet review:
998198
Full-text PDF
References | Similar Articles | Additional Information
-
[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
- Takeyuki Hida, Brownian motion, Applications of Mathematics, vol. 11, Springer-Verlag, New York-Berlin, 1980. Translated from the Japanese by the author and T. P. Speed. MR 562914
- Christian Houdré, Harmonizability, 𝑉-boundedness, (2,𝑝)-boundedness of stochastic processes, Probab. Theory Related Fields 84 (1990), no. 1, 39–54. MR 1027819, https://doi.org/10.1007/BF01288557
- Christian Houdré, Linear Fourier and stochastic analysis, Probab. Theory Related Fields 87 (1990), no. 2, 167–188. MR 1080488, https://doi.org/10.1007/BF01198428
-
[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
-
[Ph] R. S. Phillips, On Fourier-Stieltjes integrals, Trans. Amer. Math. Soc. 69 (1950), 312-323. MR 39106
- Gilles Pisier, Factorization of linear operators and geometry of Banach spaces, CBMS Regional Conference Series in Mathematics, vol. 60, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 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:
https://doi.org/10.1090/S0273-0979-1989-15830-8
