Abstract
Let {X m (t); t ∈ 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.
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*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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Zhang, R., Lin, Z. A Functional LIL for m-Fold Integrated Brownian Motion*. Chin. Ann. Math. Ser. B 27, 459–472 (2006). https://doi.org/10.1007/s11401-004-0358-z
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DOI: https://doi.org/10.1007/s11401-004-0358-z
Keywords
- m-Fold integrated Brownian motion
- Functional law of the integrated logarithm
- Small ball probability
- Weighted occupation measure