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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
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    References listed on IDEAS

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    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. Yaskov, Pavel, 2019. "On pathwise Riemann–Stieltjes integrals," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 101-107.
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    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.

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