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 Hölder 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-Chentsov condition.
Joint work with Ehsan Azmoodeh, Lauri Viitasaari, and Adil Yazigi.