DeterministicGaussianProcess

In the context of a deterministic analytic function interpreted as a deterministic Gaussian process, the (autoco)variance at 0 distance $C(0)$ could indeed be zero, as the function is deterministic and there's no randomness involved. In such a case, the relationship between the covariance function $C(h)$ and the variogram $\gamma(h)$ would simplify to:

$$ C(h) = -\gamma(h) $$