Solution (source code)

= Solution

$\boxed{(b)\longleftrightarrow P3}$. This is a <Gaussian kernel> <covariance>. Near zero, $2A^2(1-e^{-h^2/\tau^2})\sim2A^2h^2/\tau^2$, consistent with a finite mean-square derivative <variance>. The kernel has derivatives of every order, and the resulting <Gaussian process> admits a smooth version. P3 is smooth but does not repeat, unlike P1.