Necessary and sufficient conditions for continuity of hypercontractive processes and fields

Patrik Nummi and Lauri Viitasaari

Statistics & Probability Letters, 2024, vol. 208, issue C

Abstract: Sample path properties of random processes are an interesting and extensively studied topic, especially in the case of Gaussian processes. In this article, we study the continuity properties of hypercontractive fields, providing natural extensions for some known Gaussian results beyond Gaussianity. Our results apply to both random processes and random fields alike.

Keywords: Hypercontractive fields; Sample path continuity; Hölder continuity; Kolmogorov–Chentsov criterion; Sub-Weibull (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110049

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