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 引用本文: 林正炎, 程宗毛. 一类N参数Gauss过程的异常震动点集合的Hausdorff维数[J]. 应用数学和力学, 2007, 28(2): 216-224.
LIN Zheng-yan, CHENG Zong-mao. Hausdorff Dimension of the Set Generated by Exceptional Oscillations of a Class of N-Parameter Gaussian Processes[J]. Applied Mathematics and Mechanics, 2007, 28(2): 216-224.
 Citation: LIN Zheng-yan, CHENG Zong-mao. Hausdorff Dimension of the Set Generated by Exceptional Oscillations of a Class of N-Parameter Gaussian Processes[J]. Applied Mathematics and Mechanics, 2007, 28(2): 216-224.

## 一类N参数Gauss过程的异常震动点集合的Hausdorff维数

###### 作者简介:林正炎(1941- ),男,杭州人,教授,博士生导师;程宗毛(1964- ),男,江西玉山人,副教授,博士(联系人.Tel:+86-571-88235051;E-mail:zmcheng@hdu.edu.cn).
• 中图分类号: O211.6

## Hausdorff Dimension of the Set Generated by Exceptional Oscillations of a Class of N-Parameter Gaussian Processes

• 摘要: 引进了一类N参数Gauss过程,它具有比N参数Wiener过程更为一般的性质．给出了此类N参数Gauss过程的异常震动点集的定义,并且定义了此异常震动点集的Hausdorff维数．研究了此类过程的异常震动点集Hausdorff维数,给出了它的一个确切的表达式,从而获得了与Zacharie (2001)的有关两参数Wiener过程的类似的结果．考虑的参数点集是一般的超长方体．而不是Zacharie (2001)考虑的超正方体．在此更为一般的情况下,首先建立了文中引进的过程的Fernique不等式．利用此不等式和Slepian引理,证明了过程的Lévy连续模定理．Zacharie(2001)关于Hausdorff维数公式的证明依赖于两参数Wiener过程的独立增量性,而这里引进的过程不具有这种性质,因此,必须采用新的证明途径．
•  [1] Orey S,Taylor S J.How often on a Brownian path does the law of the iterated logarithm fail?[J].Proceedings of the London Mathematical Society,1974,28(1)：174-192. [2] Zacharie D.On the Hausdorff dimension of the set generated by exceptional oscillions of a two-parameter Wiener process[J].Journal of Multivariate Analysis,2001,79(1)：52-70. [3] Orey S,Pruitt W E.Sample functions of the N-parameter Wiener process[J].The Annals of Probability,1973,1(1)：138-163. [4] Lin Z Y,Choi Y K.Some limit theorems for fractional Lévy Brownian fields[J].Stochastic Processes and Their Applications,1999,82(2)：229-244. [5] Bingham N,Goldie C,Teugels J.Regular Variation[M].London: Cambridge University Press,1987. [6] Khoshnevisan D,Shi Z.Fast Sets and Points for Fractional Brownian Motion.Séminaire de Probabilitiés[M].34.Lecture Notes of Mathematics.Berlin: Springer,2000. [7] Khoshnevisan D,Peres Y,Xiao Y.Limsup random fractals[J].Electronic Journal of Probability,2000,5(4)：1-24. [8] Bradley R C.On the spectral density and asymptotic normality of weakly dependent random fields[J].Journal of Theoretical Probability,1992,5(2)：355-373.

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##### 出版历程
• 收稿日期:  2005-09-26
• 修回日期:  2006-11-13
• 刊出日期:  2007-02-15

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