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Multivariable probabilistic scale approximation. (English) Zbl 0908.41007

The authors approximate multivariate probabilistic distribution functions \(F\) by wavelet type operators of the form \[ \begin{split} B_k (F)(x_1,x_2,\dots,x_r)=\\ = \sum\limits_{j_r=-\infty}^{\infty} \dots \sum\limits_{j_1=-\infty}^{\infty} F(2^{-k} j_1,2^{-k} j_2,\dots,2^{-k} j_r) \cdot \varphi(2^k x_1-j_1,\dots,2^k x_r-j_r). \end{split} \] Conditions on \(\varphi\) are found such that \(B_k(F)\) give probabilistic distribution functions. Some sharp Jackson type inequalities are established in order to estimate the degree of approximation.
See also G. A. Anastassiou and X. M. Yu [Stochastic Anal. Appl. 10, No. 3, 251-264 (1992; Zbl 0763.41011)].
Reviewer: D.Bainov (Sofia)

MSC:

41A29 Approximation with constraints
41A63 Multidimensional problems

Citations:

Zbl 0763.41011
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