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Representation of self-similar Gaussian processes

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  • Yazigi, Adil

Abstract

We develop the canonical Volterra representation for a self-similar Gaussian process by using the Lamperti transformation of the corresponding stationary Gaussian process, where this latter one admits a canonical integral representation under the assumption of pure non-determinism. We apply the representation obtained to the equivalence in law for self-similar Gaussian processes.

Suggested Citation

  • Yazigi, Adil, 2015. "Representation of self-similar Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 94-100.
    • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:94-100
    DOI: 10.1016/j.spl.2015.01.012
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    References listed on IDEAS

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    1. Baudoin, Fabrice & Nualart, David, 2003. "Equivalence of Volterra processes," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 327-350, October.
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    Cited by:

    1. Tommi Sottinen & Lauri Viitasaari, 2018. "Parameter estimation for the Langevin equation with stationary-increment Gaussian noise," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 569-601, October.
    2. Tomoyuki Ichiba & Guodong Pang & Murad S. Taqqu, 2022. "Path Properties of a Generalized Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 35(1), pages 550-574, March.

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