Stochastic integral representation and properties of the wavelet coe cients of linear fractional stable motion
نویسندگان
چکیده
Let 0¡ 62 and let T ⊆R. Let {X (t); t ∈ T} be a linear fractional -stable (0¡ 62) motion with scaling index H (0¡H ¡ 1) and with symmetric -stable random measure. Suppose that is a bounded real function with compact support [a; b] and at least one null moment. Let the sequence of the discrete wavelet coe cients of the process X be { Dj;k = ∫ R X (t) j;k(t) dt; j; k ∈ Z } : We use a stochastic integral representation of the process X to describe the wavelet coe cients as -stable integrals when H − 1= ¿− 1. This stochastic representation is used to prove that the stochastic process of wavelet coe cients {Dj;k ; k ∈Z}, with xed scale index j∈Z, is strictly stationary. Furthermore, a property of self-similarity of the wavelet coe cients of X is proved. This property has been the motivation of several wavelet-based estimators for the scaling index H . c © 2000 Elsevier Science B.V. All rights reserved.
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تاریخ انتشار 2000