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可加布朗运动样本轨道的重分形分析 被引量：1

The Multifractal Analysis for the Sample Paths of Additive Brownian Motion
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摘要 设X={X(t):t∈RN+}为N指标可加布朗运动,其中X(t)=B1(t1)+B2(t2)+…+BN(tN), t=(t1,t2,…,tN)∈RN+,而B1,B2,…,BN为相互独立的布朗运动.讨论可加布朗运动样本轨道的重分形分析问题,得到其两类不同增量形式"α-快点"集的Hausdorff维数. Suppose X=｛X(t):t∈R^N_+｝ as the N-parameter additive Brownian motion,where X(t)=B_1(t_1)+B_2(t_2)+…+B_N(t_N),t=(t_1,t_2,…,t_N)∈R^N_+,and B_1,B_2,…,B_N denote independent Brownian motion. The aim of this note is to discuss the multifractal analysis for the sample paths of additive Brownian motion.The exact Huasdorff dimension results of 'α-fast point' sets with different increment forms of additive Brownian motion are given.
作者 邱志平 林火南
机构地区 福建师范大学数学与计算机科学学院
出处 《福建师范大学学报（自然科学版）》 CAS CSCD 2004年第4期14-19,共6页 Journal of Fujian Normal University：Natural Science Edition
基金 福建省自然科学基金资助项目(F0210015)
关键词 可加布朗运动 重分形分析 HAUSDORFF维数 additive Brownian motion multifractal analysis Hausdorff dimension
分类号 O211.6 [理学—概率论与数理统计]
  • 相关文献

参考文献7

  • 1Orey S, Taylor S J.How often on a Brownian path does the law of iterated logarithm fail[J]. Proc.London Math.Soc.,1974,28:174-192.
  • 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）,2003,19(2):1-8. 被引量：4
  • 3Ehm W. Sample fuction properties of mutli-parameter stable processes[J].Z.W.,1981, 56(2):195-228.
  • 4林火南.iener单的局部时和水平集Hausdorff测度[J].中国科学（A辑）,2000,30(10):869-880. 被引量：7
  • 5Khoshnevisan D, Shi Z.Brownian sheet and capacity[J]. Ann.Probab.,1999,27(11): 1135-1159.
  • 6Khoshnevisan D,Xiao Y M.Level sets of additive Lévy processes[J].Ann.Probab.,2002,30(1):62-100.
  • 7Falconer K J.Fractal Geometry-Mathematical Foundations and Applications[M].New York:John Wiley,1990.

二级参考文献13

  • 1胡迪鹤,刘禄勤,肖益民,吴军,赵兴球.随机分形[J].数学进展,1995,24(3):193-214. 被引量：9
  • 2Hu X, Taylor S J. The multifractal structure of stable occupation measure [J]. Stochastic Process and Their Appl. , 1997, 66: 283--299.
  • 3Shieh N R, Taylor S J. Logarithmic multifractal spectrum of stable occupation measure [J]. Stochastic Process and Their Appl., 1998, 75. 249--261.
  • 4Dembo A, Peres Y, Rosen J, et al. Thick points for planar Brownian motion and Erdoes-Taylor conjecture on random walk [J]. Acta Math., 2001, 186:239--270.
  • 5Dembo A, Peres Y, Rosen J, et al. Thick points for spatial Brownian motion. Multifractal analysis of occupation measure [J]. Ann. Probab., 2000, 28: 1--35.
  • 6Dembo A, Peres Y, Rosen J, et al.Thick points for transient symmetric stable process [J]. Elect. J. Probab. ,1999, 4: 1--18.
  • 7Dembo A, Peres Y, Rosen, J, et al. Thin points for Brownian motion [J]. Ann. Inst. H. Poincarè Math. Statist.Probab., 2000, 36: 749--774.
  • 8Orey S, Taylor S J. How often on a Brownian path does the law of iterated logarithm fail [J]. Proc. London Math.Soc., 1974, 28: 174--192.
  • 9Khoshnevisan D, Peres Y, Xiao Y M. Limsup random fractals [J]. Elect. J. Probab. , 2000, 5: 1--24.
  • 10Falconer K J. Fractal Geometry-mathematical Foundations and Applications [M]. New York: John Widely. , 1990.

共引文献6

同被引文献10

  • 1OREY S,TAYLOR S J. How often on a Brownian path does the law of iterated logarithm fail? [J]. Proc London Math Soc, 1974,28(1) : 174-192.
  • 2EHM W. Sample function properties of mutli-parameter stable processes[J]. Probability Theory and Related Fields, 1981,56(2) : 195-228.
  • 3KHOSHNEVISAN D, SHI Z. Brownian sheet and capacity[J], Ann Probab, 1999,27(3): 1135-1159.
  • 4KHOSHNEVISAN D, XIAO Y M. Level sets of additive Levy processes[J]. Ann Probab, 2002,30(1) .62-100.
  • 5FALCONER K J. Fractal geometry-mathematical foundations and application[M]. New York:John Wiley, 1990.
  • 6DEMBO A, PERES Y, ROSEN J, et al. Thick points for spatial Brownian motion.. Multifractal analysis of occupation measure[J]. Ann Probab , 2000,28 (1) : 1-35.
  • 7TRICOT C. Two definitions of fractal dimension[J]. Math Proc Cambridge Philos Soc, 1982,91(1) :57-74.
  • 8XIAO Yi-min. Packing dimension, Hausdorff dimension and Cartesian product sets[J]. Math Proc Cambridge Philos Soc, 1996,120(3) : 535-546.
  • 9林火南.iener单的局部时和水平集Hausdorff测度[J].中国科学（A辑）,2000,30(10):869-880. 被引量：7
  • 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）,2003,19(2):1-8. 被引量：4

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福建师范大学学报（自然科学版）
2004年 第4期

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