Hitting Probabilities and Fractal Dimensions of Multiparameter Multifractional Brownian Motion  

作　　者：Zhen Long CHEN 

机构地区：[1]School of Statistics and Mathematics, Zhejiang Gongshang University

出　　处：《Acta Mathematica Sinica,English Series》2013年第9期1723-1742,共20页数学学报（英文版）

基　　金：Supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. Y6100663)

摘　　要：The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an （N, d）-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an （N, d）-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.

关 键 词：Multifractional Brownian motion hitting probability inverse image level set Hausdorff dimension packing dimension 

分 类 号：O211.6[理学—概率论与数理统计]