Stochastic approximation-solvability of linear random equations involving numerical ranges.

Verma, Ram U.

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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...