Title: A remark on the multiparameter law of the iterated logarithm
Abstract: Let B ( s , t ), s , t > 0, be a Brownian sheet. In contrast to the usual law of the iterated logarithm for B , we prove that lim inf T→+∞ sup 1⩽s⩽T B(s,T/s) (2T log log T) 1 2 =a a.s. There is no analog of this limit for the Brownian motion. Generalizations of this are also discussed.