Anastassiou, G. A.; Yu, X. M. Multivariable probabilistic scale approximation. (English) Zbl 0908.41007 J. Tech. Univ. Plovdiv, Fundam. Sci. Appl., Ser. A, Pure Appl. Math. 5, 41-57 (1997). 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 Keywords:wave operators; multivariate probabilistic approximation Citations:Zbl 0763.41011 PDFBibTeX XMLCite \textit{G. A. Anastassiou} and \textit{X. M. Yu}, Izv. Tekh. Univ. Plovdiv 5, 41--57 (1997; Zbl 0908.41007)