A Functional LIL for m-Fold Integrated Brownian Motion*

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.

Keywords

m-Fold integrated Brownian motion / Functional law of the integrated logarithm / Small ball probability / Weighted occupation measure / 60F15 / 60G15 / 60G17

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