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Journal of Theoretical Probability

, Volume 32, Issue 2, pp 721–736 | Cite as

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

  • Yonghong LiuEmail author
  • Yongxiang Mo
Article
  • 38 Downloads

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.

Keywords

Fractional Brownian motion Increments Chung’s functional law of the iterated logarithm 

Mathematics Subject Classification (2010)

60F17 60F15 60G22 

Notes

Acknowledgements

The research is supported by the National Natural Science Foundation of China (NSFC) under Grant 11661025, by Science Research Foundation of Guangxi Education Department under Grant YB2014117, by Guangxi Programme for Promoting Young Teacher’s Ability under Grant 2017KY0191 and Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation.

References

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and Computing ScienceGuilin University of Electronic TechnologyGuilinChina

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