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Transactions of the American Mathematical Society

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Harmonic analysis of local times and sample functions of Gaussian processes


Author: Simeon M. Berman
Journal: Trans. Amer. Math. Soc. 143 (1969), 269-281
MSC: Primary 60.60
DOI: https://doi.org/10.1090/S0002-9947-1969-0248905-6
MathSciNet review: 0248905
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  • [1] S. M. Berman, Some continuity properties of Brownian motion with the time parameter in Hilbert space, Trans. Amer. Math. Soc. 131 (1968), 182-198. MR 0221593 (36:4645)
  • [2] -, Local times and sample function properties of stationary Gaussian processes, Trans. Amer. Math. Soc. 137 (1969), 277-300. MR 0239652 (39:1009)
  • [3] I. M. Gelfand and N. Ya. Vilenkin, Generalized functions. Vol. 4, Applications of harmonic analysis, English transl., Academic Press, New York, 1964. MR 0173945 (30:4152)
  • [4] M. B. Marcus, Hölder conditions for Gaussian processes with stationary increments, Trans. Amer. Math. Soc. 134 (1968), 29-52. MR 0230368 (37:5930)
  • [5] D. Slepian, The one-sided barrier problem for Gaussian noise, Bell System Tech. J. 41 (1962), 463-501. MR 0133183 (24:A3017)
  • [6] E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Clarendon Press, Oxford, 1937.
  • [7] J. Yeh, Differentiability of sample functions in Gaussian processes, Proc. Amer. Math. Soc. 18 (1967), 105-108; correction 19 (1968), 843. MR 0203823 (34:3670)

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DOI: https://doi.org/10.1090/S0002-9947-1969-0248905-6
Article copyright: © Copyright 1969 American Mathematical Society

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