• Communications of the Korean Mathematical Society
• /
• v.17 no.1
• /
• pp.81-93
• /
• 2002

We consider the Hausdorff measure for Brownian motion(BM) in ι$_2$. Several path properties of BM in ι$_2$ 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 ι$_2$.

• Communications of the Korean Mathematical Society
• /
• v.14 no.3
• /
• pp.569-579
• /
• 1999

We consider a random measure defined by the occupation time of Brownian motion in $l_2$. If it is normalized ${\lambda}^2$log then we show that its cluster set as ${\lambda}{longrightarrow}\infty$ can be represented by Ι-function on $\sigma$-finite measure in $l_2$.