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Approximation of the Fractional SDEs with Stochastic Forcing

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  • Kęstutis Kubilius

    (Faculty of Mathematics and Informatics, Vilnius University, Akademijos g. 4, LT-03225 Vilnius, Lithuania)

Abstract

Using the implicit Euler and Milstein approximation schemes, the conditions for the pathwise convergence rate of these approximations to the solution of the fractional SDEs with stochastic forcing are found.

Suggested Citation

  • Kęstutis Kubilius, 2024. "Approximation of the Fractional SDEs with Stochastic Forcing," Mathematics, MDPI, vol. 12(24), pages 1-22, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3875-:d:1540061
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    References listed on IDEAS

    as
    1. Falkowski, Adrian & Słomiński, Leszek, 2021. "Mean reflected stochastic differential equations with two constraints," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 172-196.
    2. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    3. Giulia Di Nunno & Kęstutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From Constant to Rough: A Survey of Continuous Volatility Modeling," Mathematics, MDPI, vol. 11(19), pages 1-35, October.
    4. Andreas Neuenkirch & Ivan Nourdin, 2007. "Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 20(4), pages 871-899, December.
    5. Fischer, Thomas & Krauss, Christopher, 2018. "Deep learning with long short-term memory networks for financial market predictions," European Journal of Operational Research, Elsevier, vol. 270(2), pages 654-669.
    6. Weiguo Liu & Jiaowan Luo, 2017. "Modified Euler approximation of stochastic differential equation driven by Brownian motion and fractional Brownian motion," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(15), pages 7427-7443, August.
    7. Kęstutis Kubilius, 2024. "The Implicit Euler Scheme for FSDEs with Stochastic Forcing: Existence and Uniqueness of the Solution," Mathematics, MDPI, vol. 12(16), pages 1-18, August.
    8. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
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