TY - JOUR
T1 - Necessary and sufficient conditions for continuity of hypercontractive processes and fields
AU - Nummi, Patrik
AU - Viitasaari, Lauri
N1 - 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
PY - 2024/5
Y1 - 2024/5
N2 - 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.
AB - 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.
KW - Hypercontractive fields
KW - Hölder continuity
KW - Kolmogorov–Chentsov criterion
KW - Sample path continuity
KW - Sub-Weibull
UR - http://www.scopus.com/inward/record.url?scp=85183616312&partnerID=8YFLogxK
U2 - 10.1016/j.spl.2024.110049
DO - 10.1016/j.spl.2024.110049
M3 - Article
AN - SCOPUS:85183616312
SN - 0167-7152
VL - 208
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
M1 - 110049
ER -