Daniel Harnett, David Nualart
Published 2012-08-09Version 1
We construct an iterated stochastic integral with fractional Brownian motion 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, 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.
On the fourth moment theorem for the complex multiple Wiener-Itô integrals
Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case $H=1/4$
Flow properties of differential equations driven by fractional Brownian motion
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