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Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 3, Pages 520–531 (Mi tvp732)  

The probability properties of bilinear expansions in Hermite polynomiels

O. V. Sarmanova, Z. N. Bratoevab

a Moscow
b Leningrad

Abstract: The present paper contains an investigation of the probability meaning of formulas (1) and (4).
According to the basic theorem 2 for sum (1) to be non negative it is nesessary and sufficient that the sequence of coefficients $\{c_k\}$ be the sequence of moments of some probability distribution in finite interval $[-1,1]$.
Some examples of densities comprised in the normal class in the sence of Fré'chet [7] are given here.

Full text: PDF file (699 kB)

English version:
Theory of Probability and its Applications, 1967, 12:3, 470–481

Bibliographic databases:

Received: 06.09.1965

Citation: O. V. Sarmanov, Z. N. Bratoeva, “The probability properties of bilinear expansions in Hermite polynomiels”, Teor. Veroyatnost. i Primenen., 12:3 (1967), 520–531; Theory Probab. Appl., 12:3 (1967), 470–481

Citation in format AMSBIB
\Bibitem{SarBra67}
\by O.~V.~Sarmanov, Z.~N.~Bratoeva
\paper The probability properties of bilinear expansions in Hermite polynomiels
\jour Teor. Veroyatnost. i Primenen.
\yr 1967
\vol 12
\issue 3
\pages 520--531
\mathnet{http://mi.mathnet.ru/tvp732}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=216541}
\zmath{https://zbmath.org/?q=an:0178.21205}
\transl
\jour Theory Probab. Appl.
\yr 1967
\vol 12
\issue 3
\pages 470--481
\crossref{https://doi.org/10.1137/1112056}


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