IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v128y2018i2p595-621.html
   My bibliography  Save this article

Distribution dependent SDEs for Landau type equations

Author

Listed:
  • Wang, Feng-Yu

Abstract

The distribution dependent stochastic differential equations (DDSDEs) describe stochastic systems whose evolution is determined by both the microcosmic site and the macrocosmic distribution of the particle. The density function associated with a DDSDE solves a nonlinear PDE. Due to the distribution dependence, some standard techniques developed for SDEs do not apply. By iterating in distributions, a strong solution is constructed using SDEs with control. By proving the uniqueness, the distribution of solutions is identified with a nonlinear semigroup Pt∗ on the space of probability measures. The exponential contraction as well as Harnack inequalities and applications are investigated for the nonlinear semigroup Pt∗ using coupling by change of measures. The main results are illustrated by homogeneous Landau equations.

Suggested Citation

  • Wang, Feng-Yu, 2018. "Distribution dependent SDEs for Landau type equations," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 595-621.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:2:p:595-621
    DOI: 10.1016/j.spa.2017.05.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414917301436
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2017.05.006?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. Arnaudon, Marc & Thalmaier, Anton & Wang, Feng-Yu, 2009. "Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3653-3670, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ning, Ning & Wu, Jing & Zheng, Jinwei, 2024. "One-dimensional McKean–Vlasov stochastic variational inequalities and coupled BSDEs with locally Hölder noise coefficients," Stochastic Processes and their Applications, Elsevier, vol. 171(C).
    2. Ren, Panpan & Wu, Jiang-Lun, 2021. "Least squares estimation for path-distribution dependent stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    3. Jianhai Bao & Xing Huang, 2022. "Approximations of McKean–Vlasov Stochastic Differential Equations with Irregular Coefficients," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1187-1215, June.
    4. Ma, Xiaocui & Yue, Haitao & Xi, Fubao, 2022. "The averaging method for doubly perturbed distribution dependent SDEs," Statistics & Probability Letters, Elsevier, vol. 189(C).
    5. Ren, Panpan, 2023. "Singular McKean–Vlasov SDEs: Well-posedness, regularities and Wang’s Harnack inequality," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 291-311.
    6. Yulin Song, 2020. "Gradient Estimates and Exponential Ergodicity for Mean-Field SDEs with Jumps," Journal of Theoretical Probability, Springer, vol. 33(1), pages 201-238, March.
    7. Xing Huang & Xiaochen Ma, 2024. "Harnack Inequality for Distribution Dependent Second-Order Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3152-3176, November.
    8. Xiao-Yu Zhao, 2024. "Well-Posedness for Path-Distribution Dependent Stochastic Differential Equations with Singular Drifts," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3654-3687, November.
    9. Yifan Bai & Xing Huang, 2023. "Log-Harnack Inequality and Exponential Ergodicity for Distribution Dependent Chan–Karolyi–Longstaff–Sanders and Vasicek Models," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1902-1921, September.
    10. Fan, Xiliang & Yu, Ting & Yuan, Chenggui, 2023. "Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 383-415.
    11. Huang, Xing & Wang, Feng-Yu, 2019. "Distribution dependent SDEs with singular coefficients," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4747-4770.
    12. Fan, Xiliang & Huang, Xing & Suo, Yongqiang & Yuan, Chenggui, 2022. "Distribution dependent SDEs driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 23-67.
    13. Sharrock, Louis & Kantas, Nikolas & Parpas, Panos & Pavliotis, Grigorios A., 2023. "Online parameter estimation for the McKean–Vlasov stochastic differential equation," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 481-546.
    14. 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).

    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. Wang, Feng-Yu & Yuan, Chenggui, 2011. "Harnack inequalities for functional SDEs with multiplicative noise and applications," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2692-2710, November.
    2. Deng, Chang-Song, 2014. "Harnack inequality on configuration spaces: The coupling approach and a unified treatment," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 220-234.
    3. Wang, Feng-Yu, 2022. "Wasserstein convergence rate for empirical measures on noncompact manifolds," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 271-287.
    4. Zong, Gaofeng & Chen, Zengjing, 2013. "Harnack inequality for mean-field stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1424-1432.
    5. Xiliang Fan, 2019. "Derivative Formulas and Applications for Degenerate Stochastic Differential Equations with Fractional Noises," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1360-1381, September.
    6. Li, Xiang-Dong, 2016. "Hamilton’s Harnack inequality and the W-entropy formula on complete Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1264-1283.
    7. Bao, Jianhai & Wang, Feng-Yu & Yuan, Chenggui, 2019. "Asymptotic Log-Harnack inequality and applications for stochastic systems of infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4576-4596.
    8. Wang, Ya & Wu, Fuke & Yin, George & Zhu, Chao, 2022. "Stochastic functional differential equations with infinite delay under non-Lipschitz coefficients: Existence and uniqueness, Markov property, ergodicity, and asymptotic log-Harnack inequality," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 1-38.
    9. Wang, Feng-Yu & Zhang, Tusheng, 2014. "Log-Harnack inequality for mild solutions of SPDEs with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1261-1274.

    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:128:y:2018:i:2:p:595-621. 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.