Abstract
We consider a general unbounded nested fractal (a typical finitely ramified self similar fractal) E ⊂ Rd. We are concerned with large time asymptotics of the Brownian motion moving on E. In particular, we show that the Donsker-Varadhan method for the one-dimensional symmetric stable process of index α still works for the present Brownian motion to identify the accumulation points of its scale changed occupation time distributions and thereby establish the law of the iterated logarithm (LIL) of Chung's type of the Brownian path and the LIL of the Brownian local time. The walk dimension dw of the Brownian motion now plays the role of α in the case of the stable process.
Published Version
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