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A strong convergence theorem for stationary Gaussian sequences in a Hilbert space


Author: Chandrakant M. Deo
Journal: Proc. Amer. Math. Soc. 79 (1980), 101-106
MSC: Primary 60B12; Secondary 60F15
DOI: https://doi.org/10.1090/S0002-9939-1980-0560593-8
MathSciNet review: 560593
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Abstract: An a.s. functional LIL is proved for stationary Gaussian sequences taking values in a Hilbert space.


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  • [1] C. R. Baker, Joint measures and cross-covariance operators, Trans. Amer. Math. Soc. 186 (1973), 273-289. MR 0336795 (49:1568)
  • [2] R. Carmona and N. Kôno, Convergence en loi du logarithme iteré pour les vecteurs gaussiens, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 36 (1976), 241-267. MR 0494354 (58:13248)
  • [3] A. H. C. Chan, M. Csörgö and P. Révész, Strassen type limit points for moving averages of a Wiener process, Canad. J. Statist. 6 (1978), 57-75. MR 521648 (82k:60061)
  • [4] M. Csörgö and P. Révész, How big are the increments of a Wiener process, Ann. Probability 7 (1979), 731-737. MR 537218 (80g:60025)
  • [5] C. M. Deo, A note on stationary Gaussian sequences, Ann. Probability 2 (1974), 954-957. MR 0378014 (51:14183)
  • [6] N. Dinculeanu. Vector measures, Pergamon Press, Berlin and New York, 1967. MR 0206190 (34:6011b)
  • [7] I. M. Gelfand and N. Ya. Vilenkin, Generalized functions, vol. 4, Academic Press, New York, 1964. MR 0435834 (55:8786d)
  • [8] I. I. Gihman and A. V. Skorohod, The theory of stochastic processes. I, Springer-Verlag, Berlin and New York, 1974. MR 0346882 (49:11603)
  • [9] J. Kuelbs, A strong convergence theorem for Banach space valued random variables, Ann. Probability 4 (1976), 744-771. MR 0420771 (54:8783)
  • [10] J. Kuelbs and R. Lepage, The law of the iterated logarithm for Brownian motion in a Banach space, Trans. Amer. Math. Soc 185 (1973), 253-264. MR 0370725 (51:6951)
  • [11] T. L. Lai, On Strassen-type laws of the iterated logarithm for delayed averages of the Wiener process, Bull. Inst. Math. Acad. Sinica 1 (1973), 29-39. MR 0321161 (47:9694)
  • [12] F. Mòricz, Probability inequalities of exponential type and laws of the iterated logarithm, Acta Sci. Math. 38 (1976), 325-341. MR 0433568 (55:6543)
  • [13] K. R. Parthasarathy, Probability measures on metric spaces, Academic Press, New York, 1967. MR 0226684 (37:2271)
  • [14] W. Philipp and W. Stout, Almost sure invariance principles for partial sums of weakly dependent random variables, Mem. Amer. Math. Soc., No. 161 (1975). MR 0433597 (55:6570)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0560593-8
Article copyright: © Copyright 1980 American Mathematical Society

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