Author： Xiao Y.
Publisher： Springer Publishing Company
ISSN： 0894-9840
Source： Journal of Theoretical Probability, Vol.11, Iss.2, 1998-04, pp. : 383-408
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Abstract
Let {W(t), t∈R} and {B(t), t≥0} be two independent Brownian motions in R with W(0) = B(0) = 0 and let Y(t)=W(B(t)) \qquad (t \ge 0) be the iterated Brownian motion. Define d-dimensional iterated Brownian motion by X(t)=(X_1(t)_{,\ldots,}X_d(t)) \qquad (t \ge 0) where X1,…, Xd are independent copies of Y. In this paper, we investigate the existence, joint continuity and Hölder conditions in the set variable of the local time L=\{L(x,B):x \in {\bf R}^d, B \in {\mathscr B}({\bf R}_+)\} of X(t), where {\mathscr B}({\bf B}_+) is the Borel -algebra of R+. These results are applied to study the irregularities of the sample paths and the uniform Hausdorff dimension of the image and inverse images of X(t).
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