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Central limit theorem for an iterated integral with respect to fBm with H>1/2

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We construct an iterated stochastic integral with respect to fractional Brownian motion (fBm) with H>1/2. The first integrand is a deterministic function, and each successive integral is with respect to an independent fBm. We show that this symmetric stochastic integral is equal to the Malliavin divergence integral. By a version of the Fourth Moment Theorem of Nualart and Peccati [10], we show that a family of such integrals converges in distribution to a scaled Brownian motion. An application is an approximation to the windings for a planar fBm, previously studied by Baudoin and Nualart [2].
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Keywords: Malliavin calculus; fractional Brownian motion; stochastic integrals

Document Type: Research Article

Affiliations: Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd, Lawrence, KS,66045-7594, USA

Publication date: March 4, 2014

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