Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T21:16:38.850Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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