Higher Order Derivatives in Costa’s Entropy Power Inequality
Higher Order Derivatives in Costa’s Entropy Power Inequality
Let X be an arbitrary continuous random variable and Z be an independent Gaussian random variable with zero mean and unit variance. For t > 0, Costa proved that e <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2h(X+√t Z)</sup> is concave in t, where the proof hinged on the first and second order derivatives of …