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If G is an orthonormal system in IL2 then for any function g (epsilon) G the function g2 is a probability density. In this paper we discuss the properties of wavelet based densities and corresponding random variables.
Brani Vidakovic
"Wavelet random variables", Proc. SPIE 3169, Wavelet Applications in Signal and Image Processing V, (30 October 1997); https://doi.org/10.1117/12.292796
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Brani Vidakovic, "Wavelet random variables," Proc. SPIE 3169, Wavelet Applications in Signal and Image Processing V, (30 October 1997); https://doi.org/10.1117/12.292796