Slepian's lemma
In probability theory, Slepian's lemma, 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