Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 219 / 3 / i / a

$\boxed{(a)⟷P2}$. The exponential covariance function gives a stationary Ornstein-Uhlenbeck process. At a small lag $h$,The variance of a difference quotient therefore diverges as $h\to 0$, so the process has no mean-square derivative. Its continuous version has rough, nondifferentiable paths, matching the jagged P2 trace in the original PDF.