About: Slepian's lemma
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In probability theory, Slepian's lemma (1962), named after David Slepian, is a Gaussian comparison inequality. It states that for Gaussian random variables and in satisfying , the following inequality holds for all real numbers : or equivalently, While this intuitive-seeming result is true for Gaussian processes, it is not in general true for other random variables—not even those with expectation 0. As a corollary, if is a centered stationary Gaussian process such that for all , it holds for any real number that
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