IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v214y2024ics0167715224001858.html
   My bibliography  Save this article

A variation of constant formula for Caputo–Hadamard fractional stochastic differential equations⋆

Author

Listed:
  • Li, Min
  • Huang, Chengming
  • Wang, Nan

Abstract

This paper studies the existence and uniqueness of the mild solutions of Caputo–Hadamard fractional stochastic differential equations (SDEs). Subsequently, a variation of constants formula is derived for these equations. The primary proof techniques rely on Itô’s isometry, the martingale representation theorem, and the adaptation of the variation of constants formula employed in deterministic Caputo–Hadamard fractional differential equations (FDEs). Furthermore, we employ the constant variation formula to investigate the mean-square stability of a class of scalar Caputo–Hadamard fractional SDEs and provide stability criteria. Consequently, this class of scalar equations can serve as basic test equations to study the stability of numerical methods for Caputo–Hadamard fractional SDEs.

Suggested Citation

  • Li, Min & Huang, Chengming & Wang, Nan, 2024. "A variation of constant formula for Caputo–Hadamard fractional stochastic differential equations⋆," Statistics & Probability Letters, Elsevier, vol. 214(C).
    • Handle: RePEc:eee:stapro:v:214:y:2024:i:c:s0167715224001858
    DOI: 10.1016/j.spl.2024.110216
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715224001858
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2024.110216?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Anh, P.T. & Doan, T.S. & Huong, P.T., 2019. "A variation of constant formula for Caputo fractional stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 351-358.
    2. Xu, Shuli & Feng, Yuqiang & Jiang, Jun & Nie, Na, 2022. "A variation of constant formula for Caputo fractional stochastic differential equations with jump–diffusion," Statistics & Probability Letters, Elsevier, vol. 185(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. Luo, Danfeng & Tian, Mengquan & Zhu, Quanxin, 2022. "Some results on finite-time stability of stochastic fractional-order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. James Hoult & Yubin Yan, 2024. "Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise," Mathematics, MDPI, vol. 12(3), pages 1-18, January.
    3. Xu, Shuli & Feng, Yuqiang & Jiang, Jun & Nie, Na, 2022. "A variation of constant formula for Caputo fractional stochastic differential equations with jump–diffusion," Statistics & Probability Letters, Elsevier, vol. 185(C).
    4. Lu, Ziqiang & Zhu, Yuanguo, 2022. "Nonlinear impulsive problems for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Huong, P.T. & The, N.T., 2023. "Well-posedness and regularity for solutions of Caputo stochastic fractional delay differential equations," Statistics & Probability Letters, Elsevier, vol. 195(C).
    6. Ahmadova, Arzu & Mahmudov, Nazim I., 2020. "Existence and uniqueness results for a class of fractional stochastic neutral differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Giacomo Ascione & Enrica Pirozzi, 2020. "On the Construction of Some Fractional Stochastic Gompertz Models," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
    8. Enrica Pirozzi, 2024. "Mittag–Leffler Fractional Stochastic Integrals and Processes with Applications," Mathematics, MDPI, vol. 12(19), pages 1-20, October.

    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:stapro:v:214:y:2024:i:c:s0167715224001858. 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/622892/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.