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Multivariate central limit theorems for averages of fractional Volterra processes and applications to parameter estimation

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Abstract

The purpose of this paper is to establish the multivariate normal convergence for the average of certain Volterra processes constructed from a fractional Brownian motion with Hurst parameter \(H > \frac{1}{2}\). Some applications to parameter estimation are then discussed.

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References

  • Breuer P, Major P (1983) Central limit theorems for non-linear functionals of Gaussian fields. J Multivar Anal 13:425–441

  • Hu Y, Nualart D (2010) Parameter estimation for fractional Ornstein-Uhlenbeck processes. Stat Probab Lett 11–12:1030–1038

    Article  MathSciNet  MATH  Google Scholar 

  • Kleptsyna ML, Le Breton A (2002) Statistical analysis of the fractional Ornstein-Uhlenbeck type process. Stat Inference Stoch Process 5:229–248

    Article  MathSciNet  MATH  Google Scholar 

  • Lin N, Lototsky SV (2014) Second order continuous-time non-stationary Gaussian autoregression. Stat Inference Stoch Process 17(1):19–49

    Article  MathSciNet  MATH  Google Scholar 

  • Nourdin I, Peccati G (2012) Normal approximations with Malliavin calculus: Stein’s Method to Universality. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Nourdin I, Peccati G, Podolskij M (2011) Quantitative Breuer-Major theorems. Stoch Process Appl 121:793–812

    Article  MathSciNet  MATH  Google Scholar 

  • Nualart D (2006) The Malliavin calculus and related topics, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  • Nualart D, Peccati G (2005) Central limit theorems for sequences of multiple stochastic integrals. Ann Probab 33(1):177–193

    Article  MathSciNet  MATH  Google Scholar 

  • Peccati G, Tudor CA (2004) Gaussian limits for vector-valued multiple stochastic integrals. Sém Probabilities XXXVIII:247–262

    MathSciNet  MATH  Google Scholar 

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Acknowledgments

We are grateful to two anonymous Referees for many helpful comments. Ivan Nourdin was partially supported by the Grant F1R-MTH-PUL-15CONF. (CONFLUENT) from Luxembourg University. David Nualart was partially supported by the NSF Grant DMS1208625 and the ARO grant FED0070445.

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Authors and Affiliations

  1. University of Kansas, Lawrence, USA

    Ivan Nourdin, David Nualart & Rola Zintout

  2. Université de Luxembourg, Walferdange, Luxembourg

    Ivan Nourdin

  3. Université de Lorraine, Vandoeuvre-lès-Nancy, France

    Rola Zintout

Authors
  1. Ivan Nourdin
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  2. David Nualart
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  3. Rola Zintout
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Correspondence to David Nualart.

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Nourdin, I., Nualart, D. & Zintout, R. Multivariate central limit theorems for averages of fractional Volterra processes and applications to parameter estimation. Stat Inference Stoch Process 19, 219–234 (2016). https://doi.org/10.1007/s11203-015-9125-x

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  • DOI: https://doi.org/10.1007/s11203-015-9125-x

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