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Discretizing the fractional Lévy area

Author

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  • Neuenkirch, A.
  • Tindel, S.
  • Unterberger, J.

Abstract

In this article, we give sharp bounds for the Euler discretization of the Lévy area associated to a d-dimensional fractional Brownian motion. We show that there are three different regimes for the exact root mean square convergence rate of the Euler scheme, depending on the Hurst parameter H[set membership, variant](1/4,1). For H 3/4 the exact rate is n-1. Moreover, we also show that a trapezoidal scheme converges (at least) with the rate n-2H+1/2. Finally, we derive the asymptotic error distribution of the Euler scheme. For H 3/4 the limit distribution is of Rosenblatt type.

Suggested Citation

  • Neuenkirch, A. & Tindel, S. & Unterberger, J., 2010. "Discretizing the fractional Lévy area," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 223-254, February.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:2:p:223-254
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    References listed on IDEAS

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    1. Neuenkirch, Andreas, 2008. "Optimal pointwise approximation of stochastic differential equations driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2294-2333, December.
    2. Baudoin, Fabrice & Coutin, Laure, 2007. "Operators associated with a stochastic differential equation driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 117(5), pages 550-574, May.
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    Cited by:

    1. Ferreiro-Castilla, Albert & Utzet, Frederic, 2011. "Lévy area for Gaussian processes: A double Wiener-Itô integral approach," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1380-1391, September.

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