대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제14권3호
  • /
  • Pages.569-579
  • /
  • 1999
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

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

  • 발행 : 1999.07.01
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초록

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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참고문헌

  1. Trans. Ann. Math. Soc. v.103 First Passage times and sojourn times for Brownion motion in space and the exact Hausdorff mneasure of the sample path Z. Ciesielski;S. J. Taylor
  2. Stochastics and Stochastic reports v.29 Exponential estimates in exit probability for some dif-fusion process in Hilbert space P. Chow;J. Menaldi
  3. Comm. on pure and Appl. Math. v.33 A law of iterated logarithm for total occupation times of transient Brownian motion M. D. Donsker;S. R. Varadhan
  4. Pacific J. Math v.41 Stochastic integrals in abstract wiener space H. Kuo
  5. Trans. Ann Math. Soc. v.185 The law of the iterated logarithm for Brownian motion in a Banach space J. Kuelbs;R. Lepage