Hitting probabilities and fractal dimensions of multiparameter multifractional Brownian motion

被引：4
作者：
Chen, Zhen Long [1 ]
机构：
[1] Zhejiang Gongshang Univ, Sch Math & Stat, Hangzhou 310018, Zhejiang, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2013年 / 29卷 / 09期
关键词：
Multifractional Brownian motion; hitting probability; inverse image; level set; Hausdorff dimension; packing dimension; SAMPLE PATH PROPERTIES;
D O I：
10.1007/s10114-013-1307-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The main goal of this paper is to study the sample path properties for the harmonisabletype 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.
引用
收藏
页码：1723 / 1742
页数：20
相关论文
共 28 条
[1]  
Ayache A, PREPRINT
[2]  
AYACHE A, 2002, P ICASSP IST
[3]   Multiparameter multifractional Brownian motion: Local nondeterminism and joint continuity of the local times [J].
Ayache, Antoine ;
Shieh, Narn-Rueih ;
Xiao, Yimin .
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2011, 47 (04) :1029-1054
[4]  
Benassi A, 1997, REV MAT IBEROAM, V13, P19
[5]   Hitting probabilities and the Hausdorff dimension of the inverse images of anisotropic Gaussian random fields [J].
Bierme, Hermine ;
Lacaux, Celine ;
Xiao, Yimin .
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2009, 41 :253-273
[6]  
Boufoussi B., 2006, Stochastics, V78, P33, DOI [10.1080/17442500600578073, DOI 10.1080/17442500600578073]
[7]   Path properties of a class of locally asymptotically self similar processes [J].
Boufoussi, Brahim ;
Dozzi, Marco ;
Guerbaz, Raby .
ELECTRONIC JOURNAL OF PROBABILITY, 2008, 13 :898-921
[8]   Sample path properties of the local time of multifractional Brownian motion [J].
Boufoussi, Brahim ;
Dozzi, Marco ;
Guerbaz, Raby .
BERNOULLI, 2007, 13 (03) :849-867
[9]   Polar functions and intersections of the random string processes [J].
Chen, Zhen Long .
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2012, 28 (10) :2067-2088
[10]   Potential theory for hyperbolic SPDEs [J].
Dalang, RC ;
Nualart, E .
ANNALS OF PROBABILITY, 2004, 32 (3A) :2099-2148
123