Hausdorff and Packing Measures of the Level Sets of Iterated Brownian Motion

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Abstract

Burdzy and Khoshnevisan(9) have shown that the Hausdorff dimension of the level sets of an iterated Brownian motion (IBM) is equal to 3/4. In this paper, the exact Hausdorff measure function and the packing measure of the levels set of IBM are given. Our approach relies on some accurate analysis on the local asymptotic of local times.

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