Slepian's lemma [SEP] named after
Slepian's lemma
In probability theory, Slepian's lemma (1962), named after David Slepian, is a Gaussian comparison inequality. It states that for Gaussian random variables formula_1 and formula_2 in formula_3 satisfying formula_4,
the following inequality holds for all real numbers formula_8:
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 formula_11 is a centered stationary Gaussian process
. He is also known for
Slepian's lemma in probability theory (1962), and for discovering a fundamental result in
distributed source coding called Slepian–Wolf coding with Jack Keil Wolf (1973).
He later joined the University of Hawaii. His father was Joseph Slepian, also a scientist. His wife is the noted children's author Jan Slepian.
Slepians.
Slepian's joint work with H.J. Landau and H.O. Pollak on discrete prolate spheroidal wave functions and sequences (DPSWF, DPSS) eventually led