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A Random Matrix Approximation for the Non-commutative Fractional Brownian Motion

Author

Listed:
  • Juan Carlos Pardo

    (Centro de Investigación en Matemáticas)

  • José-Luis Pérez

    (IIMAS-UNAM)

  • Victor Pérez-Abreu

    (Centro de Investigación en Matemáticas)

Abstract

A functional limit theorem for the empirical measure-valued process of eigenvalues of a matrix fractional Brownian motion is obtained. It is shown that the limiting measure-valued process is the non-commutative fractional Brownian motion recently introduced by Nourdin and Taqqu (J Theor Probab 27:220–248, 2014). Young and Skorohod stochastic integral techniques and fractional calculus are the main tools used.

Suggested Citation

  • Juan Carlos Pardo & José-Luis Pérez & Victor Pérez-Abreu, 2016. "A Random Matrix Approximation for the Non-commutative Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1581-1598, December.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:4:d:10.1007_s10959-015-0627-7
    DOI: 10.1007/s10959-015-0627-7
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    References listed on IDEAS

    as
    1. Nualart, David & Pérez-Abreu, Victor, 2014. "On the eigenvalue process of a matrix fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4266-4282.
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    Cited by:

    1. Aurélien Deya, 2020. "Integration with Respect to the Hermitian Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 33(1), pages 295-318, March.
    2. Song, Jian & Xiao, Yimin & Yuan, Wangjun, 2023. "On eigenvalues of the Brownian sheet matrix," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    3. Ivan Nourdin & Guangqu Zheng, 2022. "Asymptotic Behavior of Large Gaussian Correlated Wishart Matrices," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2239-2268, December.

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    2. Aurélien Deya, 2020. "Integration with Respect to the Hermitian Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 33(1), pages 295-318, March.

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