Relative Fisher information decay under Ornstein-Uhlenbeck flow
= Relative Fisher information decay under Ornstein-Uhlenbeck flow
{title2=$I(t)\leq e^{-2(t-s)}I(s)$}
The differential estimate $I'(t)\leq-2I(t)$ gives the displayed exponential bound by an integrating factor. Start at any time with finite information. Combining this with a zero limiting entropy yields $H(f_t\mid\gamma)=\int_t^\infty I(s)ds\leq I(t)/2$.