[1]邱志平,林火南.布朗单增量“快点”集的Packing维数[J].华侨大学学报(自然科学版),2011,32(1):109-112.[doi:10.11830/ISSN.1000-5013.2011.01.0109]
　QIU Zhi-ping,LIN Huo-nan.Packing Dimension of "Fast Point" Sets for Brownian Sheet[J].Journal of Huaqiao University(Natural Science),2011,32(1):109-112.[doi:10.11830/ISSN.1000-5013.2011.01.0109]
点击复制

布朗单增量“快点”集的Packing维数()
分享到：

《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第32卷
期数:
2011年第1期
页码:
109-112
栏目:
出版日期:
2011-01-20

文章信息/Info

Title:
Packing Dimension of "Fast Point" Sets for Brownian Sheet
文章编号:
1000-5013(2011)01-0109-04
作者:
邱志平; 林火南
华侨大学数学科学学院; 福建师范大学数学与计算机科学学院
Author(s):
QIU Zhi-ping1;  LIN Huo-nan2
1.School of Mathematical Sciencs, Huaqiao University, Quanzhou 362021, China 2.College of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China
关键词:
布朗单;  “快点”集;  Packing维数;  重分形分析
Keywords:
Brownian sheet;  "fast point" sets;  packing dimension;  multifractal analysis
分类号:
O211.6
DOI:
10.11830/ISSN.1000-5013.2011.01.0109
文献标志码:
A
摘要:
讨论布朗单样本轨道的重分形分析问题,通过构造一个上极限型分形集的方法,得到其不同的增量形式"快点"集的Packing维数结果.当T>0,0≤α<1,ET(α)时,有Dim(ET(α))=N,Dim(FT(α))=N,Dim(GT(α))=N,a.s..当0<α<1时,ET(α),FT(α)和GT(α)的Hausdorff维数与其Packing维数不相等.
Abstract:
The multifractal analysis for the sample paths of Brownian sheet is discussed in the paper.The packing dimensions of "fast point" sets with different increment forms of Brownian sheet are given by constructing a random fractals of limsup type.If T>0,0≤α<1,ET(α),then Dim(ET(α))=N,Dim(FT(α))=N,Dim(GT(α))=N,(a.s.).The Hausdorff dimensions of ET(α),FT(α) and GT(α) isn’t equal to their packing dimensions if 0

参考文献/References:

[1] EHM W. Sample function properties of mutli-parameter stable processes [J]. Zeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete, 1981, (2):195-228.
[2] EHM W. Sample function properties of mutli-parameter stable processes [J]. Zeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete, 1981(2):195-228.
[3] 林火南. Wiener单的局部时和水平集Hausdorff测度 [B]. 中国科学A辑, 2000, (10):869-880.
[4] 林火南. Wiener单的局部时和水平集的Hausdorff测度 [J]. 中国科学A辑, 2000, (10):869-880.doi:10.3321/j.issn:1006-9232.2000.10.002.
[5] KHOSHNEVISAN D, SHI Z. Brownian sheet and capacity [J]. Annals of Probability, 1999(3):1135-1159.
[6] KHOSHNEVISAN D, SHI Z. Brownian sheet and capacity [J]. Annals of Probability, 1999, (3):1135-1159.
[7] OREY S, PRUITT N E. Sample function of the N-parameter Wiener process [J]. Annals of Probability, 1973(1):138-163.doi:10.1214/aop/1176997030.
[8] OREY S, PRUITT N E. Sample function of the N-parameter Wiener process [J]. Annals of Probability, 1973, (1):138-163.
[9] 黄群, 林火南. 布朗单样本轨道的重分形分析 [A]. 福建师范大学学报(自然科学版), 2003, (2):1-8.
[10] 黄群, 林火南. 布朗单样本轨道的重分形分析 [J]. 福建师范大学学报（自然科学版）, 2003(2):1-8.doi:10.3969/j.issn.1000-5277.2003.02.001.
[11] 黄群. 布朗单的矩形增量快点集Hausdorff维数 [J]. 莆田学院学报, 2007(2):34-37.doi:10.3969/j.issn.1672-4143.2007.02.008.
[12] 黄群. 布朗单的矩形增量快点集Hausdorff维数 [A]. 莆田学院学报, 2007, (2):34-37, 57.
[13] FALCONER K J. Fractal geometry-mathematical foundations and application [M]. New York:John Wiley & -Sons, 1990.
[14] FALCONER K J. Fractal geometry-mathematical foundations and application [M]. New York:John Wiley & -Sons, 1990.
[15] DEMBO A, PERES Y, ROSEN J. Thick points for spatial Brownian motion:Multifractal analysis of occupation measure [J]. Annals of Probability, 2000(1):1-35.
[16] DEMBO A, PERES Y, ROSEN J. Thick points for spatial Brownian motion:Multifractal analysis of occupation measure [J]. Annals of Probability, 2000, (1):1-35.
[17] OREY S, TAYLOR S J. How often on a Brownian path does the law of iterated logarithm fail [J]. Proceedings of the London Mathematical Society, 1974(1):174-192.doi:10.1112/plms/s3-28.1.174.
[18] OREY S, TAYLOR S J. How often on a Brownian path does the law of iterated logarithm fail [J]. Proceedings of the London Mathematical Society, 1974, (1):174-192.

相似文献/References:

[1]邱志平,林火南.可加布朗运动增量“快点”集的Packing维数[J].华侨大学学报(自然科学版),2010,31(4):480.[doi:10.11830/ISSN.1000-5013.2010.04.0480]
　QIU Zhi-ping,LIN Huo-nan.Packing Dimension of "Fast Point" Sets for Additive Brownian Motion[J].Journal of Huaqiao University(Natural Science),2010,31(1):480.[doi:10.11830/ISSN.1000-5013.2010.04.0480]

备注/Memo

备注/Memo:
华侨大学科研基金资助项目(08HZR20)
更新日期/Last Update: 2014-03-23