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A multivariate central limit theorem for continuous local martingales

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  • 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
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    References listed on IDEAS

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    1. Feigin, Paul D., 1985. "Stable convergence of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 19(1), pages 125-134, February.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Federico M. Bandi & Roberto Reno, 2009. "Nonparametric Stochastic Volatility," Global COE Hi-Stat Discussion Paper Series gd08-035, Institute of Economic Research, Hitotsubashi University.
    8. 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.
    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 & 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.
    11. 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.
    12. 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.
    13. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.
    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. 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.
    16. Markus Bibinger, 2011. "Asymptotics of Asynchronicity," SFB 649 Discussion Papers SFB649DP2011-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    17. Bandi, Federico M. & Renò, Roberto, 2012. "Time-varying leverage effects," Journal of Econometrics, Elsevier, vol. 169(1), pages 94-113.
    18. 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.

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