Existence of a (non-Gaussian) process with a given covariance function

$r(\tau ) = \dfrac {\sin \tau }{\tau }$,

$r(\tau ) = \dfrac {\sin \tau }{\tau^2}$,

$r(\tau ) = \begin{cases} 1, & \tau =0, \\ 2, & \tau =1, \\ 0.5, & \tau =2, \\ 0, & \text{otherwise}, \end{cases}$

$r(\tau ) = \cos \tau$,

$r(\tau ) = e^{\left|\tau \right|}$.

$r(s, t)=e^{-\alpha \left|s-t\right|}, \alpha >0$;

$r(s, t)=2 \cos (t-s)$;

$r(s, t)=\left(1-(t-s)^{2}\right) I\left\{ \left|s-t\right| \leq 1\right\}$;

$r(s, t)=\exp \left\{ i a(s-t)-\frac{(t-s)^{2} \sigma^{2}}{2}\right\}$.