IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v188y2025ics0304414925001243.html
   My bibliography  Save this article

Averaging principle for semilinear slow–fast rough partial differential equations

Author

Listed:
  • Li, Miaomiao
  • Li, Yunzhang
  • Pei, Bin
  • Xu, Yong

Abstract

In this paper, we investigate the averaging principle for a class of semilinear slow–fast partial differential equations driven by finite-dimensional rough multiplicative noise. Specifically, the slow component is driven by a general random γ-Hölder rough path for some γ∈(1/3,1/2), while the fast component is driven by an Itô-type Brownian rough path. Using controlled rough path theory and the classical Khasminskii’s time discretization scheme, we demonstrate that the slow component converges strongly to the solution of the corresponding averaged equation under the Hölder topology.

Suggested Citation

  • Li, Miaomiao & Li, Yunzhang & Pei, Bin & Xu, Yong, 2025. "Averaging principle for semilinear slow–fast rough partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:spapps:v:188:y:2025:i:c:s0304414925001243
    DOI: 10.1016/j.spa.2025.104683
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414925001243
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2025.104683?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. Jin Feng & Jean-Pierre Fouque & Rohini Kumar, 2010. "Small-time asymptotics for fast mean-reverting stochastic volatility models," Papers 1009.2782, arXiv.org, revised Aug 2012.
    2. Fu, Hongbo & Wan, Li & Liu, Jicheng, 2015. "Strong convergence in averaging principle for stochastic hyperbolic–parabolic equations with two time-scales," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3255-3279.
    3. Ledoux, M. & Qian, Z. & Zhang, T., 2002. "Large deviations and support theorem for diffusion processes via rough paths," Stochastic Processes and their Applications, Elsevier, vol. 102(2), pages 265-283, December.
    4. Wang, Ruifang & Xu, Yong & Yue, Hongge, 2022. "Stochastic averaging for the non-autonomous mixed stochastic differential equations with locally Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 182(C).
    5. Hong, Wei & Li, Shihu & Liu, Wei, 2020. "Asymptotic log-Harnack inequality and applications for SPDE with degenerate multiplicative noise," Statistics & Probability Letters, Elsevier, vol. 164(C).
    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. Antoine Jacquier & Konstantinos Spiliopoulos, 2018. "Pathwise moderate deviations for option pricing," Papers 1803.04483, arXiv.org, revised Dec 2018.
    2. Bonesini, Ofelia & Jacquier, Antoine & Lacombe, Chloé, 2025. "A theoretical analysis of Guyon's toy volatility model," LSE Research Online Documents on Economics 127342, London School of Economics and Political Science, LSE Library.
    3. Li, Butong & Meng, Yongna & Sun, Xiaobin & Yang, Ting, 2022. "Optimal strong convergence rate for a class of McKean–Vlasov SDEs with fast oscillating perturbation," Statistics & Probability Letters, Elsevier, vol. 191(C).
    4. Blessing, Jonas & Kupper, Michael & Nendel, Max, 2023. "Convergence of Infintesimal Generators and Stability of Convex Montone Semigroups," Center for Mathematical Economics Working Papers 680, Center for Mathematical Economics, Bielefeld University.
    5. Bezemek, Z.W. & Spiliopoulos, K., 2023. "Large deviations for interacting multiscale particle systems," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 27-108.
    6. Archil Gulisashvili & Frederi Viens & Xin Zhang, 2015. "Small-time asymptotics for Gaussian self-similar stochastic volatility models," Papers 1505.05256, arXiv.org, revised Mar 2016.
    7. Jos'e E. Figueroa-L'opez & Ruoting Gong & Christian Houdr'e, 2013. "Third-Order Short-Time Expansions for Close-to-the-Money Option Prices under the CGMY Model," Papers 1305.4719, arXiv.org, revised Nov 2017.
    8. Gautier, Eric, 2005. "Uniform large deviations for the nonlinear Schrodinger equation with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1904-1927, December.
    9. Bardina, X. & Nourdin, I. & Rovira, C. & Tindel, S., 2010. "Weak approximation of a fractional SDE," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 39-65, January.
    10. Popovic, Lea, 2019. "Large deviations of Markov chains with multiple time-scales," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3319-3359.
    11. Fu, Hongbo & Wan, Li & Liu, Jicheng & Liu, Xianming, 2018. "Weak order in averaging principle for stochastic wave equation with a fast oscillation," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2557-2580.
    12. Cont, Rama & Kalinin, Alexander, 2020. "On the support of solutions to stochastic differential equations with path-dependent coefficients," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2639-2674.
    13. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559, arXiv.org.
    14. Konstantinos Spiliopoulos & Alexandra Chronopoulou, 2013. "Maximum likelihood estimation for small noise multiscale diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 16(3), pages 237-266, October.
    15. Yang, Li, 2025. "Homogenization for singularly perturbed stochastic wave equations with Hölder continuous coefficients," Statistics & Probability Letters, Elsevier, vol. 216(C).
    16. Jos'e E. Figueroa-L'opez & Ruoting Gong & Christian Houdr'e, 2012. "High-order short-time expansions for ATM option prices of exponential L\'evy models," Papers 1208.5520, arXiv.org, revised Apr 2014.
    17. Ji, Qing & Liu, Jicheng, 2025. "Strong convergence of multi-scale stochastic differential equations with a full dependence," Statistics & Probability Letters, Elsevier, vol. 216(C).
    18. Xu, Jie, 2022. "An averaging principle for slow–fast fractional stochastic parabolic equations on unbounded domains," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 358-396.
    19. Lingjiong Zhu, 2015. "Short maturity options for Azéma–Yor martingales," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-32, December.
    20. Shigeki Aida, 2024. "Rough Differential Equations Containing Path-Dependent Bounded Variation Terms," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2130-2183, September.

    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:eee:spapps:v:188:y:2025:i:c:s0304414925001243. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.