Wavelets in probability and statistics——A review in recent advances  

作　　者：XIE Zhongjie Heung Wong Wai-Cheung Ip 

机构地区：[1]School of Mathematical Sciences,Peking University,Beijing 100871,China [2]Department of Applied Mathematics,The Hong Kong Polytechnic University,Hong Kong,China

出　　处：《Chinese Science Bulletin》2002年第9期705-716,共12页

基　　金：This work was partly supported by the National Natural Science Foundation of China (Grant No. 10171005), HeungWong and Wai-Cheung Ip's research were supported by the Hong Kong Research Grants Council.

摘　　要：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- sta-tionarity, wavelet representation of Karhunen processes, hidden periodicities analysis by wavelet approach, hetero-scedasticity in wavelet regression, wavelets and neural networks, etc. are introduced in this paper. Comments, discussions and plentiful references are also involved in this review.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.

关 键 词：WAVELETS K-stationarity time VARYING SPECTRAL analysis NONLINEAR modeling WAVELET variance. 

分 类 号：O211[理学—概率论与数理统计]