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Optimality of an explicit series expansion of the fractional Brownian sheet

Author

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  • Dzhaparidze, Kacha
  • Zanten, Harry van

Abstract

We show that an explicit series expansion of the fractional Brownian motion derived by Dzhaparidze and Van Zanten (Probab. Theory Related Fields 130 (1) (2004) 39) is rate-optimal in the sense that the expected uniform norm of the truncated series vanishes at the optimal rate as the truncation point tends to infinity. The same it true for the expansion of the general fractional Brownian sheet that is obtained by a canonical extension.

Suggested Citation

  • Dzhaparidze, Kacha & Zanten, Harry van, 2005. "Optimality of an explicit series expansion of the fractional Brownian sheet," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 295-301, March.
    • Handle: RePEc:eee:stapro:v:71:y:2005:i:4:p:295-301
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    Citations

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    Cited by:

    1. Antoine Ayache & Werner Linde, 2008. "Approximation of Gaussian Random Fields: General Results and Optimal Wavelet Representation of the Lévy Fractional Motion," Journal of Theoretical Probability, Springer, vol. 21(1), pages 69-96, March.
    2. Anatoliy Malyarenko, 2008. "An Optimal Series Expansion of the Multiparameter Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 21(2), pages 459-475, June.
    3. Helga Schack, 2009. "An Optimal Wavelet Series Expansion of the Riemann–Liouville Process," Journal of Theoretical Probability, Springer, vol. 22(4), pages 1030-1057, December.
    4. Istas, Jacques, 2006. "Karhunen-Loeve expansion of spherical fractional Brownian motions," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1578-1583, August.

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