Let \(K\) be the covariance function of a stationary process on the real line such that \(K\) is twice differentiable on the diagonal, i.e.,

\[
K\left(t, t^{\prime}ight)=1-\left(t-t^{\prime}ight)^{2}+o\left(\left|t-t^{\prime}ight|^{2}ight) .
\]

Suppose that \(Y\) is stationary with covariance \(\sigma^{2} K\left(\left(t-t^{\prime}ight) / \lambdaight)\). In the long-range limit \(\lambda ightarrow \infty\) such that \(\sigma \propto \lambda\), show that \(Y\) is a random affine function.