IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i24p3875-d1540061.html
   My bibliography  Save this article

Approximation of the Fractional SDEs with Stochastic Forcing

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/24/3875/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/24/3875/
    Download Restriction: no
    ---><---

    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.
    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. Orimar Sauri, 2024. "Asymptotic Error Distribution of the Euler Scheme for Fractional Stochastic Delay Differential Equations with Additive Noise," Papers 2402.08513, arXiv.org.
    2. Giulia Di Nunno & Anton Yurchenko-Tytarenko, 2023. "Power law in Sandwiched Volterra Volatility model," Papers 2311.01228, arXiv.org.
    3. Guido Gazzani & Julien Guyon, 2024. "Pricing and calibration in the 4-factor path-dependent volatility model," Papers 2406.02319, arXiv.org.
    4. Mishari Al-Foraih & Jan Posp'iv{s}il & Josep Vives, 2023. "Computation of Greeks under rough Volterra stochastic volatility models using the Malliavin calculus approach," Papers 2312.00405, arXiv.org.
    5. Antonio Rubia & Trino-Manuel Ñíguez, 2006. "Forecasting the conditional covariance matrix of a portfolio under long-run temporal dependence," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 439-458.
    6. Asai Manabu & So Mike K.P., 2015. "Long Memory and Asymmetry for Matrix-Exponential Dynamic Correlation Processes," Journal of Time Series Econometrics, De Gruyter, vol. 7(1), pages 69-94, January.
    7. Ngene, Geoffrey & Tah, Kenneth A. & Darrat, Ali F., 2017. "Long memory or structural breaks: Some evidence for African stock markets," Review of Financial Economics, Elsevier, vol. 34(C), pages 61-73.
    8. Wei Dai & Yuan An & Wen Long, 2021. "Price change prediction of ultra high frequency financial data based on temporal convolutional network," Papers 2107.00261, arXiv.org.
    9. Shao, Zhen & Zheng, Qingru & Yang, Shanlin & Gao, Fei & Cheng, Manli & Zhang, Qiang & Liu, Chen, 2020. "Modeling and forecasting the electricity clearing price: A novel BELM based pattern classification framework and a comparative analytic study on multi-layer BELM and LSTM," Energy Economics, Elsevier, vol. 86(C).
    10. Athanasia Gavala & Nikolay Gospodinov & Deming Jiang, 2006. "Forecasting volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 381-400.
    11. Mohamed Es-Sanoun & Jude Gohou & Mounir Benboubker, 2023. "Testing of Herd Behavior In african Stock Markets During COVID-19 Pandemic [Essai de vérification du comportement mimétique dans les marchés boursiers africains au cours de la crise de covid-19]," Post-Print hal-04144289, HAL.
    12. Chiang, Thomas C., 2019. "Empirical analysis of intertemporal relations between downside risks and expected returns—Evidence from Asian markets," Research in International Business and Finance, Elsevier, vol. 47(C), pages 264-278.
    13. Kamaladdin Fataliyev & Aneesh Chivukula & Mukesh Prasad & Wei Liu, 2021. "Stock Market Analysis with Text Data: A Review," Papers 2106.12985, arXiv.org, revised Jul 2021.
    14. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
    15. Christensen, Bent Jesper & Nielsen, Morten Ørregaard & Zhu, Jie, 2015. "The impact of financial crises on the risk–return tradeoff and the leverage effect," Economic Modelling, Elsevier, vol. 49(C), pages 407-418.
    16. Chkili, Walid & Aloui, Chaker & Nguyen, Duc Khuong, 2012. "Asymmetric effects and long memory in dynamic volatility relationships between stock returns and exchange rates," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(4), pages 738-757.
    17. Harry-Paul Vander Elst, 2015. "FloGARCH: Realizing Long Memory and Asymmetries in Returns Valitility," Working Papers ECARES ECARES 2015-12, ULB -- Universite Libre de Bruxelles.
    18. Geoffrey Ngene & Ann Nduati Mungai & Allen K. Lynch, 2018. "Long-Term Dependency Structure and Structural Breaks: Evidence from the U.S. Sector Returns and Volatility," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-38, June.
    19. Asai, Manabu & McAleer, Michael, 2015. "Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance," Journal of Econometrics, Elsevier, vol. 189(2), pages 251-262.
    20. Dutta, Shantanu & Essaddam, Naceur & Kumar, Vinod & Saadi, Samir, 2017. "How does electronic trading affect efficiency of stock market and conditional volatility? Evidence from Toronto Stock Exchange," Research in International Business and Finance, Elsevier, vol. 39(PB), pages 867-877.

    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:gam:jmathe:v:12:y:2024:i:24:p:3875-:d:1540061. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.