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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



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, Hochschulbücher für Mathematik, Band 64, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. MR 0206189
    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,
  • Christian Houdré, Linear Fourier and stochastic analysis, Probab. Theory Related Fields 87 (1990), no. 2, 167–188. MR 1080488,
  • 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,
  • 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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