The fractal dimensions of the level sets of the generalized iterated Brownian motion |
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| Authors: | Chang-qing Tong Zheng-yan Lin Jing Zheng |
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| Institution: | Chang-qing TONG 1 , Zheng-yan LIN 2 , Jing ZHENG 1 1 Institute of applied mathematics, Hangzhou Dianzi University, Hangzhou 310018, China 2 Department of Mathematics, Zhejiang University, Hangzhou 310027, China |
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| Abstract: | Let {W 1(t), t ∈ R +} and {W 2(t), t ∈ R +} be two independent Brownian motions with W 1(0) = W 2(0) = 0. {H(t) = W 1(|W 2(t)|), t ∈ R +} is called a generalized iterated Brownian motion. In this paper, the Hausdorff dimension and packing dimension of the level sets $\{ t \in 0,T],H(t) = x\} $ are established for any 0 < T ≤ 1. |
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| Keywords: | Hausdorff dimension packing dimension local time generalized iterated Brownian motion |
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