• Title/Summary/Keyword: Brownian motion in ι$_2$

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ON THE HAUSDORFF MEASURE FOR A TRAJECTORY OF A BROWNIAN MOT10N IN l2

  • Cho, Nhan-Sook
    • Communications of the Korean Mathematical Society
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    • v.17 no.1
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    • pp.81-93
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    • 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$_2$.

A LAW OF ITERATED LOGARITHM FOR OCCUPATION TIME BROWNIAN IN ι$_2$

  • Cho, Nhan-Sook
    • Communications of the Korean Mathematical Society
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    • v.14 no.3
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    • pp.569-579
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    • 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 $l_2$.

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