Chinese Science Bulletin

, Volume 47, Issue 9, pp 705–716 | Cite as

Wavelets in probability and statistics—A review in recent advances

  • Xie Zhongjie 
  • Wong Heung 
  • Wai-Cheung Ip 
Review
  • 38 Downloads

Abstract

The main purpose of this paper is to give a review on recent advances of wavelet in probability and statistics. Many interesting new ideas, new results and new methods are introduced in this review. From many aspects of this paper, probability and statistics researchers may find many new interesting research topics for further studying on wavelets in stochastic processes. New results, such as K-stationarity, wavelet representation of Karhunen processes, hidden periodicities analysis by wavelet approach, heteroscedasticity in wavelet regression, wavelets and neural networks, etc. are introduced in this paper. Comments, discussions and plentiful references are also involved in this review.

Keywords

wavelets K-stationarity time varying spectral analysis nonlinear modeling wavelet variance 

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Copyright information

© Science in China Press 2002

Authors and Affiliations

  • Xie Zhongjie 
    • 1
  • Wong Heung 
    • 2
  • Wai-Cheung Ip 
    • 2
  1. 1.School of Mathematical SciencesPeking UniversityBeijingChina
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHong KongChina

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