Necessary and sufficient conditions for continuity of hypercontractive processes and fields

Patrik Nummi; Lauri Viitasaari

doi:10.1016/j.spl.2024.110049

Necessary and sufficient conditions for continuity of hypercontractive processes and fields

Patrik Nummi^*
, Lauri Viitasaari

^*Corresponding author for this work

Department of Information and Service Management

Research output: Contribution to journal › Article › Scientific › peer-review

1 Citation (Scopus)

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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.

Original language	English
Article number	110049
Journal	Statistics and Probability Letters
Volume	208
Early online date	18 Jan 2024
DOIs	https://doi.org/10.1016/j.spl.2024.110049
Publication status	Published - May 2024
MoE publication type	A1 Journal article-refereed

Funding

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). 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 ).

Keywords

Hypercontractive fields
Hölder continuity
Kolmogorov–Chentsov criterion
Sample path continuity
Sub-Weibull

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10.1016/j.spl.2024.110049Licence: CC BY

1-s2.0-S016771522400018X-mainFinal published version, 509 KBLicence: CC BY

Cite this

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title = "Necessary and sufficient conditions for continuity of hypercontractive processes and fields",

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.",

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author = "Patrik Nummi and Lauri Viitasaari",

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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

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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 - https://www.scopus.com/pages/publications/85183616312

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DO - 10.1016/j.spl.2024.110049

M3 - Article

AN - SCOPUS:85183616312

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VL - 208

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

M1 - 110049

ER -

Necessary and sufficient conditions for continuity of hypercontractive processes and fields

Abstract

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Keywords

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Lower path regularity in all dimensions

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