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Necessary and sufficient conditions for Hölder continuity of Gaussian processes

Author

Listed:
  • Azmoodeh, Ehsan
  • Sottinen, Tommi
  • Viitasaari, Lauri
  • Yazigi, Adil

Abstract

The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the Hölder continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov–Čentsov condition.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:94:y:2014:i:c:p:230-235
    DOI: 10.1016/j.spl.2014.07.030
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    Citations

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    Cited by:

    1. Pauliina Ilmonen & Soledad Torres & Lauri Viitasaari, 2020. "Oscillating Gaussian processes," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 571-593, October.
    2. 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.
    3. Giulia Di Nunno & Anton Yurchenko-Tytarenko, 2022. "Sandwiched Volterra Volatility model: Markovian approximations and hedging," Papers 2209.13054, arXiv.org, revised Jul 2024.
    4. 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.
    5. 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.
    6. Giulia Di Nunno & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2022. "Option pricing in Sandwiched Volterra Volatility model," Papers 2209.10688, arXiv.org, revised Jul 2024.
    7. Giulia Di Nunno & Anton Yurchenko-Tytarenko, 2023. "Power law in Sandwiched Volterra Volatility model," Papers 2311.01228, arXiv.org.
    8. 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.
    9. Krzysztof Bisewski & Krzysztof Dȩbicki & Tomasz Rolski, 2022. "Derivative of the expected supremum of fractional Brownian motion at $$H=1$$ H = 1," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 53-68, October.
    10. Nummi, Patrik & Viitasaari, Lauri, 2024. "Necessary and sufficient conditions for continuity of hypercontractive processes and fields," Statistics & Probability Letters, Elsevier, vol. 208(C).
    11. Maleki Almani, Hamidreza & Shokrollahi, Foad & Sottinen, Tommi, 2024. "Prediction of Gaussian Volterra processes with compound Poisson jumps," Statistics & Probability Letters, Elsevier, vol. 208(C).
    12. Sottinen, Tommi & Viitasaari, Lauri, 2017. "Prediction law of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 155-166.
    13. 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.

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