Necessary and Sufficient Conditions for H\"older Continuity of Gaussian Processes

The continuity of Gaussian processes is extensively studied topic and it culminates in the Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the H"older continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov-\v{C}entsov condition.