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Necessary and sufficient conditions for Hölder continuity of Gaussian processes
Institution:1. Faculté des Sciences, de la Technologie et de la Communication, Université du Luxembourg, P.O. Box L-1359, Luxembourg;2. Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, FIN-65101 Vaasa, Finland;3. Department of Mathematics and System Analysis, Aalto University School of Science, Helsinki, P.O. Box 11100, FIN-00076 Aalto, Finland;1. Department of Surgery, Anne Arundel Medical Center, Johns Hopkins University School of Medicine, Annapolis, MD;2. Department of Surgery, University of Maryland School of Medicine, Baltimore, MD;3. Department of Surgery, Carolinas Medical Center, Charlotte, NC;1. University of Pittsburgh, United States;2. University of Haifa, Israel
Abstract:The continuity of Gaussian processes is an extensively studied topic and it culminates in 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–?entsov condition.
Keywords:Gaussian processes  Hölder continuity  Kolmogorov–?entsov condition  Self-similar processes
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