On the Hausdorff measure for a trajectory of a Brownian motion in $l_2$
Commun. Korean Math. Soc. 2002 Vol. 17, No. 1, 81-93 Printed March 1, 2002
Nhansook Cho Hansung University
Abstract : We consider the Hausdorff measure for Brownian motion(BM) in $l_2$. Several path properties of BM in $l_2$ are used to show the upper bound of Hausdorff measure. We also show the lower bound of it applying a law of iterated logarithm for the occupation time of BM in $l_2$.
Keywords : Hausdorff measure, Brownian motion in $l_2$