Random periodic point and fixed point results for random monotone mappings in ordered Polish spaces.

Zhu, Xing-Hua; Xiao, Jian-Zhong

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On a characterization of orthogonality with respect to particular sequences of random variables in $L^{2}$

Umberto Triacca, Andrei Volodin (2010)

Applications of Mathematics

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This note deals with the orthogonality between sequences of random variables. The main idea of the note is to apply the results on equidistant systems of points in a Hilbert space to the case of the space $L^{2} (Ω, ℱ, ℙ)$ of real square integrable random variables. The main result gives a necessary and sufficient condition for a particular sequence of random variables (elements of which are taken from sets of equidistant elements of $L^{2} (Ω, ℱ, ℙ)$ ) to be orthogonal to some other sequence in $L^{2} (Ω, ℱ, ℙ)$ . The result obtained...