Necessary and sufficient conditions for continuity of hypercontractive processes and fields

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2024-05
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Mcode
Degree programme
Language
en
Pages
Series
Statistics and Probability Letters, Volume 208
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.
Description
Funding Information: PN acknowledges support by the Academy of Finland (grant agreement No 323099) and the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 818437). Funding Information: PN acknowledges support by the Academy of Finland (grant agreement No 323099 ) and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 818437 ). Publisher Copyright: © 2024 The Authors
Keywords
Hypercontractive fields, Hölder continuity, Kolmogorov–Chentsov criterion, Sample path continuity, Sub-Weibull
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Citation
Nummi, P & Viitasaari, L 2024, ' Necessary and sufficient conditions for continuity of hypercontractive processes and fields ', Statistics and Probability Letters, vol. 208, 110049 . https://doi.org/10.1016/j.spl.2024.110049