Solution
= Solution
$\boxed{(a)\longleftrightarrow P2}$. The <exponential covariance function> gives a stationary <Ornstein-Uhlenbeck process>. At a small lag $h$,
$$
\mathbb E[(f(t+h)-f(t))^2]=2A^2(1-e^{-|h|/\tau})\sim\frac{2A^2}{\tau}|h|.
$$
The <variance> of a difference quotient therefore diverges as $h\to0$, so the process has no mean-square derivative. Its continuous version has rough, nondifferentiable paths, matching the jagged P2 trace in the original PDF.