[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):480-482.[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(4):480-482.[doi:10.11830/ISSN.1000-5013.2010.04.0480]
点击复制

可加布朗运动增量“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31卷
期数:
2010年第4期
页码:
480-482
栏目:
出版日期:
2010-07-20

文章信息/Info

Title:
Packing Dimension of "Fast Point" Sets for Additive Brownian Motion
文章编号:
1000-5013(2010)04-0480-03
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 Sciences, Huaqiao University, Quanzhou 362021, China; 2.School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China
关键词:
可加布朗运动;  “快点”集;  Packing维数;  重分形分析
Keywords:
additive Brownian motion;  "fast point" sets;  Packing dimension;  multifractal analysis
分类号:
O211.6
DOI:
10.11830/ISSN.1000-5013.2010.04.0480
文献标志码:
A
摘要:
讨论可加布朗运动样本轨道的重分形分析问题.利用构造上极限型集,集的乘积的Packing维数和Hausdorff维数关系的方法,分别得到其局部增量和沿坐标方向增量两种不同增量形式"快点"集的Packing维数结果.
Abstract:
The multifractal analysis for the sample paths of additive Brownian motion is discussed in this paper.The Packing dimension of "fast point" sets determined by the local increment and by the incerment in the direction of coordinate for additive Brownian motion are obtained respectively by means of constructing a limsup random set and the relation between Packing dimension and Hausdorff dimension of the Product sets.

参考文献/References:

[1] 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.
[2] 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.
[3] EHM W. Sample function properties of mutli-parameter stable processes [J]. Probability Theory and Related Fields, 1981(2):195-228.
[4] 林火南. Wiener单的局部时和水平集的Hausdorff测度 [J]. 中国科学D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.doi:10.1214/aop/1022677442.
[6] KHOSHNEVISAN D, XIAO Y M. Level sets of additive Lévy processes [J]. Annals of Probability, 2002(1):62-100.
[7] 邱志平, 林火南. 可加布朗运动样本轨道的重分形分析 [J]. 福建师范大学学报(自然科学版), 2004(4):14-19.doi:10.3969/j.issn.1000-5277.2004.04.004.
[8] FALCONER K J. Fractal geometry-mathematical foundations and application [M]. New York:John Wiley and Sons, Inc, 1990.
[9] 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.
[10] TRICOT C. Two definitions of fractal dimension [J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1982(1):57-74.doi:10.1017/S0305004100059119.
[11] XIAO Yi-min. Packing dimension, Hausdorff dimension and Cartesian product sets [J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1996(3):535-546.doi:10.1017/S030500410007506X.

相似文献/References:

[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.[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(4):109.[doi:10.11830/ISSN.1000-5013.2011.01.0109]

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