IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v50y2000i3p229-235.html
   My bibliography  Save this article

A multivariate central limit theorem for continuous local martingales

Author

Listed:
  • van Zanten, Harry

Abstract

A theorem on the weak convergence of a properly normalized multivariate continuous local martingale is proved. The time-change theorem used for this purpose allows for short and transparent arguments.

Suggested Citation

  • van Zanten, Harry, 2000. "A multivariate central limit theorem for continuous local martingales," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 229-235, November.
    • Handle: RePEc:eee:stapro:v:50:y:2000:i:3:p:229-235
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(00)00108-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Feigin, Paul D., 1985. "Stable convergence of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 19(1), pages 125-134, February.
    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. Federico M. Bandi & Roberto Reno, 2009. "Nonparametric Stochastic Volatility," Global COE Hi-Stat Discussion Paper Series gd08-035, Institute of Economic Research, Hitotsubashi University.
    2. Emmanuel Gobet & Gustaw Matulewicz, 2017. "Parameter estimation of Ornstein–Uhlenbeck process generating a stochastic graph," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 211-235, July.
    3. Bandi, Federico M. & Renò, Roberto, 2012. "Time-varying leverage effects," Journal of Econometrics, Elsevier, vol. 169(1), pages 94-113.
    4. Matyas Barczy & Balazs Nyul & Gyula Pap, 2015. "Least squares estimation for the subcritical Heston model based on continuous time observations," Papers 1511.05948, arXiv.org, revised Aug 2018.
    5. Matyas Barczy & Gyula Pap, 2013. "Asymptotic properties of maximum likelihood estimators for Heston models based on continuous time observations," Papers 1310.4783, arXiv.org, revised Jun 2015.
    6. Gaïffas, Stéphane & Matulewicz, Gustaw, 2019. "Sparse inference of the drift of a high-dimensional Ornstein–Uhlenbeck process," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 1-20.
    7. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.
    8. Barczy, Mátyás & Ben Alaya, Mohamed & Kebaier, Ahmed & Pap, Gyula, 2018. "Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1135-1164.
    9. Matyas Barczy & Leif Doering & Zenghu Li & Gyula Pap, 2013. "Parameter estimation for a subcritical affine two factor model," Papers 1302.3451, arXiv.org, revised Apr 2014.
    10. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2016. "Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations," Papers 1609.05865, arXiv.org, revised Aug 2017.
    11. Beáta Bolyog & Gyula Pap, 2019. "On conditional least squares estimation for affine diffusions based on continuous time observations," Statistical Inference for Stochastic Processes, Springer, vol. 22(1), pages 41-75, April.
    12. Aït-Sahalia, Yacine & Park, Joon Y., 2016. "Bandwidth selection and asymptotic properties of local nonparametric estimators in possibly nonstationary continuous-time models," Journal of Econometrics, Elsevier, vol. 192(1), pages 119-138.
    13. Bibinger, Markus, 2011. "Asymptotics of asynchronicity," SFB 649 Discussion Papers 2011-033, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    14. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2015. "Asymptotic behavior of maximum likelihood estimators for a jump-type Heston model," Papers 1509.08869, arXiv.org, revised May 2018.
    15. Choi, Hwan-sik & Jeong, Minsoo & Park, Joon Y., 2014. "An asymptotic analysis of likelihood-based diffusion model selection using high frequency data," Journal of Econometrics, Elsevier, vol. 178(P3), pages 539-557.
    16. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2017. "Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations," Papers 1711.02140, arXiv.org, revised Feb 2019.
    17. Friedrich Hubalek & Petra Posedel, 2008. "Asymptotic analysis for a simple explicit estimator in Barndorff-Nielsen and Shephard stochastic volatility models," Papers 0807.3479, arXiv.org.
    18. Giovanni Peccati & Murad S. Taqqu, 2008. "Stable Convergence of Multiple Wiener-Itô Integrals," Journal of Theoretical Probability, Springer, vol. 21(3), pages 527-570, September.
    19. repec:hum:wpaper:sfb649dp2011-033 is not listed 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. Crimaldi, Irene & Dai Pra, Paolo & Minelli, Ida Germana, 2016. "Fluctuation theorems for synchronization of interacting Pólya’s urns," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 930-947.
    2. Giovanni Peccati & Murad S. Taqqu, 2008. "Stable Convergence of Multiple Wiener-Itô Integrals," Journal of Theoretical Probability, Springer, vol. 21(3), pages 527-570, September.
    3. Crimaldi, Irene & Pratelli, Luca, 2005. "Convergence results for multivariate martingales," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 571-577, April.
    4. Küchler, Uwe & Sørensen, Michael M., 1998. "A note on limit theorems for multivariate martingales," SFB 373 Discussion Papers 1998,45, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Nakahiro Yoshida, 1990. "Asymptotic behavior of M-estimator and related random field for diffusion process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 221-251, June.
    6. Bibinger, Markus, 2011. "Asymptotics of asynchronicity," SFB 649 Discussion Papers 2011-033, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Teo Sharia, 2010. "Recursive parameter estimation: asymptotic expansion," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(2), pages 343-362, April.

    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:50:y:2000:i:3:p:229-235. 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.