IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v177y2021ics0167715221001279.html
   My bibliography  Save this article

A probabilistic representation for heat flow of harmonic map on manifolds with time-dependent Riemannian metric

Author

Listed:
  • Chen, Xin
  • Ye, Wenjie

Abstract

In this paper we will give a probabilistic representation for the heat flow of harmonic map with time-dependent Riemannian metric via a forward–backward stochastic differential equation on Riemannian manifolds. Moreover, we can provide an alternative stochastic method for the proof of existence of a unique local solution for heat flow of harmonic map with time-dependent Riemannian metric.

Suggested Citation

  • Chen, Xin & Ye, Wenjie, 2021. "A probabilistic representation for heat flow of harmonic map on manifolds with time-dependent Riemannian metric," Statistics & Probability Letters, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:stapro:v:177:y:2021:i:c:s0167715221001279
    DOI: 10.1016/j.spl.2021.109165
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715221001279
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2021.109165?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. Guo, Hongxin & Philipowski, Robert & Thalmaier, Anton, 2014. "A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3535-3552.
    2. Ping He & Yong Ren & Defei Zhang, 2020. "A Study on a New Class of Backward Stochastic Differential Equation," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, May.
    3. Ma, Jin & Yin, Hong & Zhang, Jianfeng, 2012. "On non-Markovian forward–backward SDEs and backward stochastic PDEs," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 3980-4004.
    4. Wu, Zhen & Yu, Zhiyong, 2014. "Probabilistic interpretation for a system of quasilinear parabolic partial differential equation combined with algebra equations," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 3921-3947.
    5. Kupper, Michael & Luo, Peng & Tangpi, Ludovic, 2019. "Multidimensional Markovian FBSDEs with super-quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 902-923.
    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. Luis Escauriaza & Daniel C. Schwarz & Hao Xing, 2020. "Radner equilibrium and systems of quadratic BSDEs with discontinuous generators," Papers 2008.03500, arXiv.org, revised May 2021.
    2. Pei Zhang & Adriana Irawati Nur Ibrahim & Nur Anisah Mohamed, 2023. "Anticipated BSDEs Driven by Fractional Brownian Motion with a Time-Delayed Generator," Mathematics, MDPI, vol. 11(23), pages 1-13, December.
    3. Bernt {O}ksendal & Agn`es Sulem, 2015. "Optimal control of predictive mean-field equations and applications to finance," Papers 1505.04921, arXiv.org.
    4. Yang, Xue & Zhang, Qi & Zhang, Tusheng, 2020. "Reflected backward stochastic partial differential equations in a convex domain," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6038-6063.
    5. Ludovic Tangpi & Xuchen Zhou, 2022. "Optimal Investment in a Large Population of Competitive and Heterogeneous Agents," Papers 2202.11314, arXiv.org, revised Feb 2023.
    6. Nam, Kihun, 2021. "Locally Lipschitz BSDE driven by a continuous martingale a path-derivative approach," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 376-411.
    7. Stefan Ankirchner & Alexander Fromm & Thomas Kruse & Alexandre Popier, 2018. "Optimal position targeting via decoupling fields," Working Papers hal-01500311, HAL.
    8. Hernández, Camilo, 2023. "On quadratic multidimensional type-I BSVIEs, infinite families of BSDEs and their applications," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 249-298.
    9. Pei Zhang & Nur Anisah Mohamed & Adriana Irawati Nur Ibrahim, 2023. "Mean-Field and Anticipated BSDEs with Time-Delayed Generator," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    10. Holger Kraft & Thomas Seiferling & Frank Thomas Seifried, 2017. "Optimal consumption and investment with Epstein–Zin recursive utility," Finance and Stochastics, Springer, vol. 21(1), pages 187-226, January.
    11. Alexander Fromm, 2019. "Evaluation of equity-based debt obligations," Papers 1901.02254, arXiv.org.
    12. Martin Herdegen & Johannes Muhle-Karbe & Dylan Possamaï, 2021. "Equilibrium asset pricing with transaction costs," Finance and Stochastics, Springer, vol. 25(2), pages 231-275, April.
    13. Ulrich Horst & Jinniao Qiu & Qi Zhang, 2014. "A Constrained Control Problem with Degenerate Coefficients and Degenerate Backward SPDEs with Singular Terminal Condition," Papers 1407.0108, arXiv.org, revised Jul 2015.
    14. Qiu, Jinniao, 2017. "Weak solution for a class of fully nonlinear stochastic Hamilton–Jacobi–Bellman equations," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1926-1959.

    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:177:y:2021:i:c:s0167715221001279. 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.