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Journal of Theoretical Probability

, Volume 31, Issue 4, pp 2032–2055 | Cite as

LLN for Quadratic Forms of Long Memory Time Series and Its Applications in Random Matrix Theory

  • Pavel Yaskov
Article
  • 186 Downloads

Abstract

We obtain a weak law of large numbers for quadratic forms of a stationary regular time series, imposing no rate of convergence to zero of its covariance function. We show how this law can be applied in proving universality properties of limiting spectral distributions of sample covariance matrices. In particular, we give another derivation of a recent result of Merlevède and Peligrad, who studied sample covariance matrices generated by IID samples of long memory time series.

Keywords

Quadratic forms Long memory Random matrices Sample covariance matrices 

Mathematics Subject Classification (2010)

60B20 

Notes

Acknowledgements

The author thanks an anonymous reviewer for constructive comments that improved the paper.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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