The Fractal Dimensions of the Level Sets of the Generalized Iterated Brownian Motion  

作　　者：Chang-qing TONG Zheng-yan LIN Jing ZHENG 

机构地区：[1]Institute of applied mathematics,Hangzhou Dianzi University [2]Department of Mathematics,Zhejiang University

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第3期597-602,共6页应用数学学报（英文版）

基　　金：Supported by the National Science Foundation of Zhejiang(No.LQ12F03003)

摘　　要：Let{W1（t）, t∈R＋} and {W2（t）, t∈R＋} be two independent Brownian motions with W1（0） = W2（0） = 0. {H （t） = W1（｜W2（t）｜）, t ∈R＋} is called a generalized iterated Brownian motion. In this paper, the Hausdorff dimension and packing dimension of the level sets {t ∈[0, T ], H（t） = x} are established for any 0 T ≤ 1.Let{W1（t）, t∈R＋} and {W2（t）, t∈R＋} be two independent Brownian motions with W1（0） = W2（0） = 0. {H （t） = W1（｜W2（t）｜）, t ∈R＋} is called a generalized iterated Brownian motion. In this paper, the Hausdorff dimension and packing dimension of the level sets {t ∈[0, T ], H（t） = x} are established for any 0 T ≤ 1.

关 键 词：Hausdorff dimension packing dimension local time generalized iterated Brownian motion 

分 类 号：O211.6[理学—概率论与数理统计]