Can continuous-time stationary stable processes have discrete linear representations?

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• 作者：Pipiras ; Vladas ; Taqqu ; Murad S. ; Abry ; Patrice
• 关键词：primary 60G52 ; secondary 60G10 ; 60G18 ; 28D ; 37A ; Stable processes ; Self-similarity ; Stationarity ; Minimal spectral representations ; Flows ; Cocycles
• 刊名：Statistics and Probability Letters
• 出版年：2003
• 出版时间：August 15, 2003
• 年：2003
• 卷：64
• 期：2
• 页码：147-157
• 全文大小：265 K

文摘

We show that a non-trivial continuous-time strictly Cannot display formula is a collection of deterministic functions and {?_n}_nZ are independent strictly α-stable random variables. Analogous results hold for self-similar strictly α-stable processes and for strictly α-stable processes with stationary increments. As a consequence, the usual wavelet decomposition of Gaussian self-similar processes cannot be extended to the α-stable, α<2 case.