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| A Functional LIL for m-Fold Integrated Brownian Motion |
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Citation： |
Rongmao ZHANG,Zhengyan LIN.A Functional LIL for m-Fold Integrated Brownian Motion[J].Chinese Annals of Mathematics B,2006,27(4):459~472 |
| Page view： 1060
Net amount： 813 |
Authors： |
Rongmao ZHANG; Zhengyan LIN |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10131040) and the Specialized
Research Fund for the Doctor Program of Higher Education (No.2002335090). |
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| Abstract： |
Let $\{X_{m}(t), t\in R_{+}\}$ 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. |
Keywords： |
m-Fold integrated Brownian motion, Functional law of the integrated
logarithm, Small ball probability, Weighted occupation measure |
Classification： |
60F15, 60G15, 60G17 |
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