Strassen's law for weighted sup-norms

R. Norvaiša

Institute of Mathematics and Informatics, Lithuania

Abstract: Let $S$ be a partial sum process based on a sequence of independent identically distributed mean 0 and variance 1 random variables. We prove that the sequence $\{(2nLLn)^{-1/2}S(n, \cdot );n\ge1\}$ satisfies the functional law of the iterated logarithm with respect to a weighted $\sup$-norm whenever the limit set is compact.

Keywords: Strassen's law of the iterated logarithm, partial sums process, Strassen's set.

Received: 10.03.1994
Revised: 12.05.1996

Language: English

DOI: 10.4213/tvp2596

 English version: Theory of Probability and its Applications, 1998, 42:4, 646–655

Bibliographic databases:

• 
• 
•