IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v208y2024ics016771522400018x.html
   My bibliography  Save this article

Necessary and sufficient conditions for continuity of hypercontractive processes and fields

Author

Listed:
  • Nummi, Patrik
  • Viitasaari, Lauri

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.

Suggested Citation

  • Nummi, Patrik & Viitasaari, Lauri, 2024. "Necessary and sufficient conditions for continuity of hypercontractive processes and fields," Statistics & Probability Letters, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:stapro:v:208:y:2024:i:c:s016771522400018x
    DOI: 10.1016/j.spl.2024.110049
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771522400018X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2024.110049?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hu, Yaozhong & Le, Khoa, 2013. "A multiparameter Garsia–Rodemich–Rumsey inequality and some applications," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3359-3377.
    2. Barigozzi, Matteo & Hallin, Marc, 2020. "Generalized dynamic factor models and volatilities: Consistency, rates, and prediction intervals," Journal of Econometrics, Elsevier, vol. 216(1), pages 4-34.
    3. Azmoodeh, Ehsan & Sottinen, Tommi & Viitasaari, Lauri & Yazigi, Adil, 2014. "Necessary and sufficient conditions for Hölder continuity of Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 230-235.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    2. Tommi Sottinen & Lauri Viitasaari, 2018. "Parameter estimation for the Langevin equation with stationary-increment Gaussian noise," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 569-601, October.
    3. Carlos Trucíos & João H. G. Mazzeu & Marc Hallin & Luiz K. Hotta & Pedro L. Valls Pereira & Mauricio Zevallos, 2022. "Forecasting Conditional Covariance Matrices in High-Dimensional Time Series: A General Dynamic Factor Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 40-52, December.
    4. Giulia Di Nunno & Anton Yurchenko-Tytarenko, 2022. "Sandwiched Volterra Volatility model: Markovian approximations and hedging," Papers 2209.13054, arXiv.org, revised Jul 2024.
    5. Matteo Barigozzi, 2023. "Asymptotic equivalence of Principal Components and Quasi Maximum Likelihood estimators in Large Approximate Factor Models," Papers 2307.09864, arXiv.org, revised Jun 2024.
    6. Barigozzi, Matteo & Hallin, Marc & Luciani, Matteo & Zaffaroni, Paolo, 2024. "Inferential theory for generalized dynamic factor models," Journal of Econometrics, Elsevier, vol. 239(2).
    7. Hallin, Marc & Trucíos, Carlos, 2023. "Forecasting value-at-risk and expected shortfall in large portfolios: A general dynamic factor model approach," Econometrics and Statistics, Elsevier, vol. 27(C), pages 1-15.
    8. Mohamed Omari, 2023. "An α-Order Fractional Brownian Motion with Hurst Index H ∈ (0,1) and α ∈ R + $\alpha \in \mathbbm {R}_{+}$," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 572-599, February.
    9. Marc Hallin, 2022. "Manfred Deistler and the General-Dynamic-Factor-Model Approach to the Statistical Analysis of High-Dimensional Time Series," Econometrics, MDPI, vol. 10(4), pages 1-9, December.
    10. Tomoyuki Ichiba & Guodong Pang & Murad S. Taqqu, 2022. "Path Properties of a Generalized Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 35(1), pages 550-574, March.
    11. Giulia Di Nunno & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2022. "Option pricing in Sandwiched Volterra Volatility model," Papers 2209.10688, arXiv.org, revised Jul 2024.
    12. Trucíos, Carlos & Mazzeu, João H.G. & Hotta, Luiz K. & Valls Pereira, Pedro L. & Hallin, Marc, 2021. "Robustness and the general dynamic factor model with infinite-dimensional space: Identification, estimation, and forecasting," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1520-1534.
    13. Maleki Almani, Hamidreza & Shokrollahi, Foad & Sottinen, Tommi, 2024. "Prediction of Gaussian Volterra processes with compound Poisson jumps," Statistics & Probability Letters, Elsevier, vol. 208(C).
    14. Michele Giordano & Anton Yurchenko-Tytarenko, 2024. "Optimal control in linear-quadratic stochastic advertising models with memory," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 275-298, June.
    15. Hu, Yaozhong & Lê, Khoa & Mytnik, Leonid, 2017. "Stochastic differential equation for Brox diffusion," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2281-2315.
    16. Jianqing Fan & Ricardo Masini & Marcelo C. Medeiros, 2021. "Bridging factor and sparse models," Papers 2102.11341, arXiv.org, revised Sep 2022.
    17. Chen, Zhe & Leskelä, Lasse & Viitasaari, Lauri, 2019. "Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2723-2757.
    18. Carlos Cesar Trucios-Maza & João H. G Mazzeu & Luis K. Hotta & Pedro L. Valls Pereira & Marc Hallin, 2019. "On the robustness of the general dynamic factor model with infinite-dimensional space: identification, estimation, and forecasting," Working Papers ECARES 2019-32, ULB -- Universite Libre de Bruxelles.
    19. Marc Hallin & Carlos Trucíos, 2020. "Forecasting Value-at-Risk and Expected Shortfall in Large Portfolios: a General Dynamic Factor Approach," Working Papers ECARES 2020-50, ULB -- Universite Libre de Bruxelles.
    20. Giulia Di Nunno & Anton Yurchenko-Tytarenko, 2023. "Power law in Sandwiched Volterra Volatility model," Papers 2311.01228, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:208:y:2024:i:c:s016771522400018x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.