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On Bernstein-type inequalities for martingales

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  • Dzhaparidze, K.
  • van Zanten, J. H.

Abstract

Bernstein-type inequalities for local martingales are derived. The results extend a number of well-known exponential inequalities and yield an asymptotic inequality for a sequence of asymptotically continuous martingales.

Suggested Citation

  • Dzhaparidze, K. & van Zanten, J. H., 2001. "On Bernstein-type inequalities for martingales," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 109-117, May.
    • Handle: RePEc:eee:spapps:v:93:y:2001:i:1:p:109-117
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    References listed on IDEAS

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    1. Liptser, R. & Spokoiny, V., 2000. "Deviation probability bound for martingales with applications to statistical estimation," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 347-357, February.
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    Cited by:

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    2. Christensen, Kim & Oomen, Roel & Renò, Roberto, 2022. "The drift burst hypothesis," Journal of Econometrics, Elsevier, vol. 227(2), pages 461-497.
    3. Sason, Igal, 2013. "Tightened exponential bounds for discrete-time conditionally symmetric martingales with bounded jumps," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1928-1936.
    4. Michael Diether, 2012. "Wavelet estimation in diffusions with periodicity," Statistical Inference for Stochastic Processes, Springer, vol. 15(3), pages 257-284, October.
    5. Fan, Xiequan & Grama, Ion & Liu, Quansheng, 2012. "Hoeffding’s inequality for supermartingales," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3545-3559.
    6. Pepin, Bob, 2021. "Concentration inequalities for additive functionals: A martingale approach," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 103-138.
    7. Löcherbach, Eva & Orlandi, Enza, 2011. "Neighborhood radius estimation for variable-neighborhood random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2151-2185, September.
    8. Ruijun Bu & Jihyun Kim & Bin Wang, 2020. "Uniform and Lp Convergences of Nonparametric Estimation for Diffusion Models," Working Papers 202021, University of Liverpool, Department of Economics.
    9. Reinhard Höpfner & Yury Kutoyants, 2010. "Estimating discontinuous periodic signals in a time inhomogeneous diffusion," Statistical Inference for Stochastic Processes, Springer, vol. 13(3), pages 193-230, October.
    10. Naiqi Liu & Vladimir V. Ulyanov & Hanchao Wang, 2022. "On De la Peña Type Inequalities for Point Processes," Mathematics, MDPI, vol. 10(12), pages 1-13, June.
    11. Bu, Ruijun & Kim, Jihyun & Wang, Bin, 2023. "Uniform and Lp convergences for nonparametric continuous time regressions with semiparametric applications," Journal of Econometrics, Elsevier, vol. 235(2), pages 1934-1954.

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