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Fractional Processes and Their Statistical Inference: An Overview

Abstract

We give an overview of properties of fractional processes such as fractional Brownian motion, mixed fractional Brownian motion, sub-fractional Brownian motion, fractional Lévy process , fractional Poisson process and present a short review of problems of statistical inference for processes driven by fractional processes.

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Acknowledgements

Work presented in this paper is supported under the “INSA Senior Scientist” scheme at the CR Rao Advanced Institute of Mathematics, Statistics and Computer Science, Hyderabad, India. The author thanks the referees for their exhaustive review and Prof. Arni Srinivasa Rao for inviting him to contribute to this Special Issue of the Journal of Indian Institute of Science on Probability and Statistics.

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Correspondence to B. L. S. Prakasa Rao.

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Prakasa Rao, B.L.S. Fractional Processes and Their Statistical Inference: An Overview. J Indian Inst Sci (2022). https://doi.org/10.1007/s41745-021-00271-z

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  • DOI: https://doi.org/10.1007/s41745-021-00271-z

Keywords

  • Fractional Brownian motion
  • Fractional Lévy process
  • Fractional Poisson process
  • Mixed fractional Brownian motion
  • Sub-fractional Brownian motion

Mathematics Subject Classification

  • Primary 60G22