Open Access
August, 1985 The LIL when $X$ is in the Domain of Attraction of a Gaussian Law
J. Kuelbs
Ann. Probab. 13(3): 825-859 (August, 1985). DOI: 10.1214/aop/1176992910


If $X$ takes values in a Banach space $B$ and is in the domain of normal attraction of a Gaussian law on $B$ with $EX = 0, E(\|X\|^2/L_2\|X\|) < \infty$, then it is known that $X$ satisfies the compact law of the iterated logarithm as described in Goodman, Kuelbs and Zinn [9], Theorem 4.1. In this paper the analogous result is demonstrated when $X$ is merely in the domain of attraction of a Gaussian law. The functional LIL is also obtained in this setting. These results refine Corollary 7 of Kuelbs and Zinn [22], as well as various functional LILs.


Download Citation

J. Kuelbs. "The LIL when $X$ is in the Domain of Attraction of a Gaussian Law." Ann. Probab. 13 (3) 825 - 859, August, 1985.


Published: August, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0572.60010
MathSciNet: MR799424
Digital Object Identifier: 10.1214/aop/1176992910

Primary: 60B05
Secondary: 28C20 , 60B10 , 60B11 , 60B12 , 60F10 , 60F15

Keywords: cluster set , domain of attraction of a Gaussian random variable , Law of the iterated logarithm

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 3 • August, 1985
Back to Top