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The law of the iterated logarithm for Brownian sheets

Published online by Cambridge University Press:  14 July 2016

W. J. Park
W. J. Park*
Affiliation:
Wright State University, Dayton, Ohio
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Abstract

Strassen-type law of the iterated logarithm for Brownian sheets presented by Pyke [7] is proved by using recent results of Kuelbs and Lepage [4]: the law of the iterated logarithm for Brownian motion in a Banach space and some applications are given.

Keywords

BROWNIAN SHEETSLAW OF THE ITERATED LOGARITHMBROWNIAN MOTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 4 , December 1975 , pp. 840 - 844
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Fernique, X. (1965) Continuité de certains processus Gaussiens. Sem. R. fortet, Inst. Henri Poincaré, Paris. Google Scholar
[2] Gross, L. Lectures in modern analysis and applications II. Lecture Notes in Math. Vol. 140, Springer-Verlag, New York.Google Scholar
[3] Kuelbs, J. (1973) The invariance principle for Banach space valued random variables. J. Multivariate Analysis 3, 161–172.Google Scholar
[4] Kuelbs, J. and Lepage, R. (1973) The law of the iterated logarithm for Brownian motion in a Banach space. Trans. Amer. Math. Soc. 183, 253–264.Google Scholar
[5] Park, W. J. (1970) A multi-parameter Gaussian process. Ann. Math. Statist. 41, 1582–1595.CrossRefGoogle Scholar
[6] Park, W. J. (1974) On Strassen's version of the law of the iterated logarithm for the two-parameter Gaussian process. J. Multivariate Analysis 4, 479–485.Google Scholar
[7] Pyke, R. (1972) Partial sums of matrix arrays and Brownian sheets. Stochastic Geometry and Stochastic Analysis , ed Harding, E. F. and Kendall, D. G. Wiley, New York.Google Scholar
[8] Strassen, V. (1964) An invariance principle for the law of the iterated logarithm. Z. Wahrscheinlichkeitsth. 3, 211–266.Google Scholar