Chinese Annals of Mathematics, Series B

, Volume 27, Issue 4, pp 459–472 | Cite as

A Functional LIL for m-Fold Integrated Brownian Motion*

  • Rongmao Zhang
  • Zhengyan Lin


Let {X m (t); tR +} be an m-Fold integrated Brownian motion. In this paper, with the help of small ball probability estimate, a functional law of the iterated logarithm (LIL) for X m (t) is established. This extends the classic Chung type liminf result for this process. Furthermore, a result about the weighted occupation measure for X m (t) is also obtained.


m-Fold integrated Brownian motion Functional law of the integrated logarithm Small ball probability Weighted occupation measure 

2000 MR Subject Classification

60F15 60G15 60G17 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang University (Xixi Campus)Hangzhou 310028China
  2. 2.School of Mathematical SciencesPeking UniversityBeijing 100871China

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