Discretizing the fractional Lévy area

A. Neuenkirch, S. Tindel and J. Unterberger

Stochastic Processes and their Applications, 2010, vol. 120, issue 2, 223-254

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.

Keywords: Fractional; Brownian; motion; Lévy; area; Discretization; schemes; Asymptotic; error; distribution (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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