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Hausdorff and packing measures of the level sets of iterated Brownian motion. (English) Zbl 0935.60066
Iterated Brownian motion is defined as $$Z(t)=X(Y(t))$$ where $$X$$ and $$Y$$ are independent (two-sided) Brownian motions. The exact Hausdorff dimension gauge of the level sets of iterated Bronwian motion is determined to be $$\varphi(x)=x^{3/4}[\log\log(1/x)]^{3/4}$$. This result generalizes earlier work of K. Burdzy and D. Khoshnevisan [in: Séminaire de probabilités XXIX. Lect. Notes Math. 1613, 231-236 (1995; Zbl 0853.60061)]. The paper also contains a slightly less precise result about the packing gauge of the level sets. The proofs rely on an accurate analysis of the local times.

##### MSC:
 60J65 Brownian motion 28A78 Hausdorff and packing measures 60J55 Local time and additive functionals
Zbl 0853.60061
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