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Bulletin of the American Mathematical Society

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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
MathSciNet review: 998198
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  • S. Bochner, Stationarity, boundedness, almost periodicity of random-valued functions, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. II, University of California Press, Berkeley and Los Angeles, 1956, pp. 7–27. MR 0084883
  • Harald Cramér, On harmonic analysis in certain functional spaces, Ark. Mat. Astr. Fys. 28B (1942), no. 12, 7. MR 0006609
  • N. Dinculeanu, Vector measures, International Series of Monographs in Pure and Applied Mathematics, Vol. 95, Pergamon Press, Oxford-New York-Toronto, Ont.; VEB Deutscher Verlag der Wissenschaften, Berlin, 1967. MR 0206190
  • I. M. Gel’fand and N. Ya. Vilenkin, Generalized functions. Vol. 4: Applications of harmonic analysis, Translated by Amiel Feinstein, Academic Press, New York - London, 1964, 1964. MR 0173945
  • 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, 10.1007/BF01288557
  • Christian Houdré, Linear Fourier and stochastic analysis, Probab. Theory Related Fields 87 (1990), no. 2, 167–188. MR 1080488, 10.1007/BF01198428
  • Igor Kluvánek, Characterization of Fourier-Stieltjes transforms of vector and operator valued measures, Czechoslovak Math. J. 17 (92) (1967), 261–277 (English, with Russian summary). MR 0230872
  • Hannu Niemi, On orthogonally scattered dilations of bounded vector measures, Ann. Acad. Sci. Fenn. Ser. A I Math. 3 (1977), no. 1, 43–51. MR 0632060
  • R. S. Phillips, On Fourier-Stieltjes integrals, Trans. Amer. Math. Soc. 69 (1950), 312–323. MR 0039106, 10.1090/S0002-9947-1950-0039106-0
  • 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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DOI: https://doi.org/10.1090/S0273-0979-1989-15830-8