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Chung’s Functional Law of the Iterated Logarithm for Increments of a Fractional Brownian Motion

Author

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  • Yonghong Liu

    (Guilin University of Electronic Technology)

  • Yongxiang Mo

    (Guilin University of Electronic Technology)

Abstract

In this paper, we present Chung’s functional law of the iterated logarithm for increments of a fractional Brownian motion. The corresponding results in Gao and Wang (Stat Probab Lett 73:165–177, 2005), Monrad and Rootzén (Probab Theory Relat Fields 101:173–192, 1995) and Wang (J Theor Probab 18(2):327–343, 2005) are extended. The main tools in the proof are large deviations and small deviations for fractional Brownian motion.

Suggested Citation

  • Yonghong Liu & Yongxiang Mo, 2019. "Chung’s Functional Law of the Iterated Logarithm for Increments of a Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 32(2), pages 721-736, June.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:2:d:10.1007_s10959-018-0866-5
    DOI: 10.1007/s10959-018-0866-5
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    References listed on IDEAS

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    1. Ortega, Joaquín, 1984. "On the size of the increments of nonstationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 18(1), pages 47-56, September.
    2. Wensheng Wang, 2005. "Functional Limit Theorems for the Increments of Gaussian Samples," Journal of Theoretical Probability, Springer, vol. 18(2), pages 327-343, April.
    3. Gao, Fuqing & Wang, Qinghua, 2005. "The rate of convergence in the functional limit theorem for increments of a Brownian motion," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 165-177, June.
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