A Fractional Donsker Theorem

Abstract

We prove a Donsker-type approximation of the fractional Brownian motion which extends a result by Sottinen for the case H > 1/2 to the full range of Hurst parameters H ∈ (0, 1). The convergence is established by a Donsker-type theorem for Volterra Gaussian processes. The approximation is applied to weak convergence of fractional Wiener integrals.

Keywords:

• Fractional Brownian motion
• Invariance principle
• Weak convergence

Mathematics Subject Classification:

• Primary: 60F17, 60G22
• Secondary: 60G15

Acknowledgments

The author thanks Christian Bender for helpful discussions and comments.

Notes

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