Continuity of Gaussian processes
Continuity of Gaussian processes
We give a proof of Ferniqueâs theorem that if X is a stationary Gaussian process and ${\sigma ^2}(h) = E{(X(h) - X(0))^2}$ then X has continuous sample paths provided that, for some $\varepsilon > 0,\sigma (h) \leqq \psi (h),0 \leqq h \leqq \varepsilon$, where $\psi$ is any increasing function satisfying …