IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v38y2025i3d10.1007_s10959-025-01422-z.html
   My bibliography  Save this article

Discretization of integrals driven by multifractional Brownian motions with discontinuous integrands

Author

Listed:
  • Kostiantyn Ralchenko

    (University of Vaasa
    Taras Shevchenko National University of Kyiv)

  • Foad Shokrollahi

    (University of Vaasa)

  • Tommi Sottinen

    (University of Vaasa)

Abstract

We establish the rate of convergence in the $$L^1$$ L 1 -norm for equidistant approximations of stochastic integrals with discontinuous integrands driven by multifractional Brownian motion. Our findings extend the known results for the case when the driver is a fractional Brownian motion.

Suggested Citation

  • Kostiantyn Ralchenko & Foad Shokrollahi & Tommi Sottinen, 2025. "Discretization of integrals driven by multifractional Brownian motions with discontinuous integrands," Journal of Theoretical Probability, Springer, vol. 38(3), pages 1-26, September.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:3:d:10.1007_s10959-025-01422-z
    DOI: 10.1007/s10959-025-01422-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-025-01422-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-025-01422-z?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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Ehsan Azmoodeh & Pauliina Ilmonen & Nourhan Shafik & Tommi Sottinen & Lauri Viitasaari, 2024. "On Sharp Rate of Convergence for Discretization of Integrals Driven by Fractional Brownian Motions and Related Processes with Discontinuous Integrands," Journal of Theoretical Probability, Springer, vol. 37(1), pages 721-743, March.
    3. Ehsan Azmoodeh & Lauri Viitasaari, 2015. "Rate of Convergence for Discretization of Integrals with Respect to Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 28(1), pages 396-422, March.
    4. Marco Dozzi & Yuriy Kozachenko & Yuliya Mishura & Kostiantyn Ralchenko, 2018. "Asymptotic growth of trajectories of multifractional Brownian motion, with statistical applications to drift parameter estimation," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 21-52, April.
    5. Tommi Sottinen & Lauri Viitasaari, 2016. "Pathwise Integrals and Itô–Tanaka Formula for Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 29(2), pages 590-616, June.
    6. Stoev, Stilian A. & Taqqu, Murad S., 2006. "How rich is the class of multifractional Brownian motions?," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 200-221, February.
    7. Yaskov, Pavel, 2019. "On pathwise Riemann–Stieltjes integrals," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 101-107.
    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. Ehsan Azmoodeh & Pauliina Ilmonen & Nourhan Shafik & Tommi Sottinen & Lauri Viitasaari, 2024. "On Sharp Rate of Convergence for Discretization of Integrals Driven by Fractional Brownian Motions and Related Processes with Discontinuous Integrands," Journal of Theoretical Probability, Springer, vol. 37(1), pages 721-743, March.
    2. Christian Bender & Joachim Lebovits & Jacques Lévy Véhel, 2024. "General Transfer Formula for Stochastic Integral with Respect to Multifractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 37(1), pages 905-932, March.
    3. Bardet, Jean-Marc & Surgailis, Donatas, 2013. "Nonparametric estimation of the local Hurst function of multifractional Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1004-1045.
    4. Anderes, Ethan B. & Stein, Michael L., 2011. "Local likelihood estimation for nonstationary random fields," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 506-520, March.
    5. Loboda, Dennis & Mies, Fabian & Steland, Ansgar, 2021. "Regularity of multifractional moving average processes with random Hurst exponent," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 21-48.
    6. Dai, Hongshuai & Li, Yuqiang, 2010. "A weak limit theorem for generalized multifractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 348-356, March.
    7. Balança, Paul, 2015. "Some sample path properties of multifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3823-3850.
    8. Peng, Qidi & Zhao, Ran, 2018. "A general class of multifractional processes and stock price informativeness," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 248-267.
    9. 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.
    10. Balança, Paul & Herbin, Erick, 2012. "2-microlocal analysis of martingales and stochastic integrals," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2346-2382.
    11. Ehsan Azmoodeh & Ozan Hur, 2023. "Generalized Families of Fractional Stochastic Dominance," Papers 2307.08651, arXiv.org, revised Feb 2025.
    12. Cohen, Serge & Lacaux, Céline & Ledoux, Michel, 2008. "A general framework for simulation of fractional fields," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1489-1517, September.
    13. Ayache, Antoine & Louckx, Christophe, 2025. "Harmonizable Multifractional Stable Field: Sharp results on sample path behavior," Stochastic Processes and their Applications, Elsevier, vol. 186(C).
    14. Lavancier, Frédéric & Philippe, Anne & Surgailis, Donatas, 2009. "Covariance function of vector self-similar processes," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2415-2421, December.
    15. Xavier Brouty & Matthieu Garcin & Hugo Roccaro, 2024. "Estimation of bid-ask spreads in the presence of serial dependence," Papers 2407.17401, arXiv.org, revised Jan 2025.
    16. Lebovits, Joachim & Lévy Véhel, Jacques & Herbin, Erick, 2014. "Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 678-708.
    17. Wensheng Wang, 2024. "The Moduli of Continuity for Operator Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2097-2120, September.
    18. Joachim Lebovits & Mark Podolskij, 2016. "Estimation of the global regularity of a multifractional Brownian motion," CREATES Research Papers 2016-33, Department of Economics and Business Economics, Aarhus University.
    19. Marco Dozzi & Yuriy Kozachenko & Yuliya Mishura & Kostiantyn Ralchenko, 2018. "Asymptotic growth of trajectories of multifractional Brownian motion, with statistical applications to drift parameter estimation," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 21-52, April.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:jotpro:v:38:y:2025:i:3:d:10.1007_s10959-025-01422-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.