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Maximum likelihood estimator for the sub-fractional Brownian motion approximated by a random walk

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Abstract

We estimate the drift parameter in a simple linear model driven by sub-fractional Brownian motion. We construct a maximum likelihood estimator (MLE) for the drift parameter by using a random walk approximation of the sub-fractional Brownian motion and study the asymptotic behaviors of the estimator. Simulations confirm the theoretical results and indicate superiority of the new proposed estimator.

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Acknowledgments

The authors would like to thank the Associate Editor and Reviewers for their careful reading and comments. Those comments and suggestions are valuable and very helpful for revising and improving the manuscript. In addition, the authors are very grateful to Professor F.Q. Gao for the useful discussions.

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Authors and Affiliations

  1. School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, Hunan , 411201, People’s Republic of China

    Nenghui Kuang

  2. School of Mathematics and Statistics, Wuhan University, Wuhan , 430072, People’s Republic of China

    Nenghui Kuang & Huantian Xie

  3. School of Science, Linyi University, Linyi, Shandong , 276005, People’s Republic of China

    Huantian Xie

Authors
  1. Nenghui Kuang
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  2. Huantian Xie
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Corresponding author

Correspondence to Nenghui Kuang.

Additional information

Research supported by the National Natural Science Foundation of China under Grant 11101137 and 11126188.

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Kuang, N., Xie, H. Maximum likelihood estimator for the sub-fractional Brownian motion approximated by a random walk. Ann Inst Stat Math 67, 75–91 (2015). https://doi.org/10.1007/s10463-013-0439-4

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  • DOI: https://doi.org/10.1007/s10463-013-0439-4

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