Logarithmically concave function: Difference between revisions

Revision as of 22:00, 9 May 2012

Revision as of 21:11, 7 July 2012

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:is log-concave (see [[Prékopa–Leindler inequality]]).

* This implies that [[convolution]] preserves log-concavity, since {{math|''h''(''x'',''y'')}} = {{math|''f''(''x'' -''y'') ''g''(''y'')}} is log-concave if {{math|''f''}} and {{math|''g''}} are log-concave, and therefore

::<math>(f*g)(x)=\int f(x-y)g(y) dy = \int h(x,y) dy</math>