A strong convergence theorem for stationary Gaussian sequences in a Hilbert space
HTML articles powered by AMS MathViewer
- by Chandrakant M. Deo PDF
- Proc. Amer. Math. Soc. 79 (1980), 101-106 Request permission
Abstract:
An a.s. functional LIL is proved for stationary Gaussian sequences taking values in a Hilbert space.References
- Charles R. Baker, Joint measures and cross-covariance operators, Trans. Amer. Math. Soc. 186 (1973), 273–289. MR 336795, DOI 10.1090/S0002-9947-1973-0336795-3
- René Carmona and Norio Kôno, Convergence en loi et lois du logarithme itéré pour les vecteurs gaussiens, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 36 (1976), no. 3, 241–267 (French). MR 494354, DOI 10.1007/BF00532548
- A. H. C. Chan, M. Csörgő, and P. Révész, Strassen type limit points for moving averages of a Wiener process, Canad. J. Statist. 6 (1978), no. 1, 57–75 (English, with French summary). MR 521648, DOI 10.2307/3314826
- M. Csörgő and P. Révész, How big are the increments of a Wiener process?, Ann. Probab. 7 (1979), no. 4, 731–737. MR 537218
- Chandrakant M. Deo, A note on stationary Gaussian sequences, Ann. Probability 2 (1974), 954–957. MR 378014, DOI 10.1214/aop/1176996561
- N. Dinculeanu, Vector measures, Hochschulbücher für Mathematik, Band 64, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. MR 0206189
- I. M. Gel′fand and G. E. Shilov, Generalized functions. Vol. 1, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1964 [1977]. Properties and operations; Translated from the Russian by Eugene Saletan. MR 0435831
- Ĭ. Ī. Gīhman and A. V. Skorohod, The theory of stochastic processes. I, Die Grundlehren der mathematischen Wissenschaften, Band 210, Springer-Verlag, New York-Heidelberg, 1974. Translated from the Russian by S. Kotz. MR 0346882
- J. Kuelbs, A strong convergence theorem for Banach space valued random variables, Ann. Probability 4 (1976), no. 5, 744–771. MR 420771, DOI 10.1214/aop/1176995982
- J. Kuelbs and R. Lepage, The law of the iterated logarithm for Brownian motion in a Banach space, Trans. Amer. Math. Soc. 185 (1973), 253–265. MR 370725, DOI 10.1090/S0002-9947-1973-0370725-3
- Tze-Leung Lai, On Strassen-type laws of the iterated logarithm for delayed averages of the Wiener process, Bull. Inst. Math. Acad. Sinica 1 (1973), no. 1, 29–39. MR 321161
- F. Móricz, Probability inequalities of exponential type and laws of the iterated logarithm, Acta Sci. Math. (Szeged) 38 (1976), no. 3-4, 325–341. MR 433568
- K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, No. 3, Academic Press, Inc., New York-London, 1967. MR 0226684
- Walter Philipp and William Stout, Almost sure invariance principles for partial sums of weakly dependent random variables, Mem. Amer. Math. Soc. 2 (1975), no. 161,, 161, iv+140. MR 433597, DOI 10.1090/memo/0161
Additional Information
- © Copyright 1980 American Mathematical Society
- 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