IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v274y2016icp237-246.html
   My bibliography  Save this article

Maximum likelihood estimation of McKean–Vlasov stochastic differential equation and its application

Author

Listed:
  • Wen, Jianghui
  • Wang, Xiangjun
  • Mao, Shuhua
  • Xiao, Xinping

Abstract

McKean–Vlasov stochastic differential equation is a class of complicated and special equation since the drift term is a function of stochastic process and its distribution. This paper discusses the maximum likelihood estimation of parameters in the drift term through transforming McKean–Vlasov stochastic process into homogeneous one and estimates parameters of the latter to discuss that of McKean–Vlasov equation. Then we build a McKean–Vlasov stochastic model for ion diffusion since ions moved by liquid viscous force and also by coulomb interaction related with ion charged distribution, and simulate the changing trajectory of the ion motion through numerical calculation. Results manifest that the ion motion shows strong random property and has the same tendency for different time intervals, however, the smaller of time lag, the more distinct of wave trajectory observed.

Suggested Citation

  • Wen, Jianghui & Wang, Xiangjun & Mao, Shuhua & Xiao, Xinping, 2016. "Maximum likelihood estimation of McKean–Vlasov stochastic differential equation and its application," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 237-246.
    • Handle: RePEc:eee:apmaco:v:274:y:2016:i:c:p:237-246
    DOI: 10.1016/j.amc.2015.11.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315014812
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.11.019?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. Asaf Cohen, 2015. "Parameter Estimation: The Proper Way to Use Bayesian Posterior Processes with Brownian Noise," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 361-389, February.
    2. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    3. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    4. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
    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. Della Maestra, Laetitia & Hoffmann, Marc, 2023. "The LAN property for McKean–Vlasov models in a mean-field regime," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 109-146.
    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. Amorino, Chiara & Heidari, Akram & Pilipauskaitė, Vytautė & Podolskij, Mark, 2023. "Parameter estimation of discretely observed interacting particle systems," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 350-386.
    4. 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.

    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. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers math/0411034, arXiv.org.
    2. Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations. Working paper #2," NCER Working Paper Series 2, National Centre for Econometric Research.
    3. A. S. Hurn & J. I. Jeisman & K. A. Lindsay, 0. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 390-455.
    4. Christian Gourieroux & Hung T. Nguyen & Songsak Sriboonchitta, 2017. "Nonparametric estimation of a scalar diffusion model from discrete time data: a survey," Annals of Operations Research, Springer, vol. 256(2), pages 203-219, September.
    5. Li, Minqiang, 2010. "A damped diffusion framework for financial modeling and closed-form maximum likelihood estimation," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 132-157, February.
    6. Dennis Kristensen, 2007. "Nonparametric Estimation and Misspecification Testing of Diffusion Models," CREATES Research Papers 2007-01, Department of Economics and Business Economics, Aarhus University.
    7. Song, Zhaogang, 2011. "A martingale approach for testing diffusion models based on infinitesimal operator," Journal of Econometrics, Elsevier, vol. 162(2), pages 189-212, June.
    8. Ngoc-Khanh Tran, 2019. "The Functional Stochastic Discount Factor," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 1-49, December.
    9. Choi, Seungmoon, 2013. "Closed-form likelihood expansions for multivariate time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, vol. 174(2), pages 45-65.
    10. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    11. Helle Sørensen, 2002. "Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey," Discussion Papers 02-08, University of Copenhagen. Department of Economics.
    12. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    13. Phillips, Peter C.B. & Yu, Jun, 2009. "A two-stage realized volatility approach to estimation of diffusion processes with discrete data," Journal of Econometrics, Elsevier, vol. 150(2), pages 139-150, June.
    14. Egorov, Alexei V. & Li, Haitao & Xu, Yuewu, 2003. "Maximum likelihood estimation of time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, vol. 114(1), pages 107-139, May.
    15. Ruijun Bu & Ludovic Giet & Kaddour Hadri & Michel Lubrano, 2009. "Modeling Multivariate Interest Rates using Time-Varying Copulas and Reducible Stochastic Differential Equations," Working Papers halshs-00408014, HAL.
    16. Kristensen, Dennis, 2010. "Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models," Journal of Econometrics, Elsevier, vol. 156(2), pages 239-259, June.
    17. João Nicolau, 2002. "A new technique for simulating the likelihood of stochastic differential equations," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 91-103, June.
    18. Jaime A. Londoño, 2003. "Parametric Estimation Of Diffusion Processes Sampled At First Exit Time," Econometrics 0305002, University Library of Munich, Germany, revised 16 Feb 2004.
    19. Bandi, Federico M., 2002. "Short-term interest rate dynamics: a spatial approach," Journal of Financial Economics, Elsevier, vol. 65(1), pages 73-110, July.
    20. Michael Sørensen, 2008. "Parametric inference for discretely sampled stochastic differential equations," CREATES Research Papers 2008-18, Department of Economics and Business Economics, Aarhus University.

    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:apmaco:v:274:y:2016:i:c:p:237-246. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.