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

LIN Zheng-yan; CHENG Zong-mao

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Article Navigation > Applied Mathematics and Mechanics > 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.

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

LIN Zheng-yan¹,
CHENG Zong-mao^1,2

1.
Department of Mathematics, Zhejiang University, Hangzhou 310028, P. R. China;

Received Date: 2005-09-26
Rev Recd Date: 2006-11-13
Publish Date: 2007-02-15

Abstract

Abstract

A class of N-parameter Gaussian processes were introduced,which are more general than the N-parameter Wiener process.The definition of the set generated by exceptional oscillations of class of these processes was given.And then the Hausdorff dimension of this set was defined.The Hausdorff dimensions of these processes were studied and an exact representative for them was given,which is similar to that for the two-parameter Wiener process by Zacharie (2001).Moreover,the time set considered is a hyperrectangle which is more general than a hyper-square used by Zacharie (2001).For this more general case,a Fernique-type inequality was established and then using this inequality and the Slepian lemma,a Lvy's continuity modulus theorem was shown.Independence of increments is required for showing the representative of the Hausdorff dimension by Zacharie (2001).This property is absent for the processes introduced here,so a different way is to be found.
- N -parameter Gaussian process,
- modulus of continuity,
- Hausdorff dimension

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References(8)

References

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