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Some liminf results on increments of fractional Brownian motion

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References

  1. E. Csáki and P. Révész, How big must be the increments of a Wiener process? Acta Math. Acad. Sci. Hungar., 33 (1979), 37–49.

    Google Scholar 

  2. M. Csörgö and P. Révész, Strong Approximations in Probability and Statistics, Academic Press (New York, 1981).

    Google Scholar 

  3. Hong Shengyan, Some results on increments of Gaussian processes, Acta Mathematica Sinica, 11A (1990), 137–146.

    Google Scholar 

  4. C. G. Khatri, On certain inequalities for normal distributions and their applications to simultaneous confidence bounds, Acat Math. Stat., 38 (1967), 1853–1867.

    Google Scholar 

  5. J. Kuelbs, W. V. Li and Q. M. Shao, Small ball probability for Gaussian processes with stationary increments under Hölder norms. Preprint (1993).

  6. Z. Y. Lin and C. R. Lu, Strong Limit Theorems, Kluwer Academic Publishers (Dordrecht-Beijing, 1992).

    Google Scholar 

  7. D. Monrad and H. Rootzén, Small values of Gaussian processes and functional laws of the iterated logarithm, Probab. Theory Rel. Fields, 101 (1995), 173–192.

    Google Scholar 

  8. J. Ortega, On the size of the increments of non-stationary Gaussian processes, Stochastic Processes Their Appl., 18 (1984), 47–56.

    Google Scholar 

  9. D. Slepian, The one-sided barrier problem for Gaussian noise, Bell System Tech. J., 41 (1962), 463–501.

    Google Scholar 

  10. Q. M. Shao, A note on increments of a Wiener process, J. Math. Sinica, 6 (1986), 175–182 (in Chinese).

    Google Scholar 

  11. Q. M. Shao, A note on small probability of a Gaussian process with stationary increments, J. Theor. Probab., 6 (1993), 595–602.

    Google Scholar 

  12. C. Qualls and H. Watanabe, Asymptotic properties of Gaussian processes, Ann. Math. Stat., 43 (1972), 580–596.

    Google Scholar 

  13. P. Révész, On the increments of Wiener and related processes, Ann. Probab., 10 (1982), 613–622.

    Google Scholar 

  14. Z. Sidák, On multivariate normal probabilities of rectangles: their dependence on correlation, Ann. Math. Stat., 39 (1968), 1425–1434.

    Google Scholar 

  15. Q. M. Shao and D. Wang, Small ball probabilities of Gaussian fields. Preprint (1993).

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Zhang, LX. Some liminf results on increments of fractional Brownian motion. Acta Math Hung 71, 215–240 (1996). https://doi.org/10.1007/BF00052111

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  • DOI: https://doi.org/10.1007/BF00052111

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