CLT for an iterated integral with respect to fBm with H > 1/2
Probability
2013-04-29 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1208.1908,
title = {CLT for an iterated integral with respect to fBm with H > 1/2},
author = {Daniel Harnett and David Nualart},
journal= {arXiv preprint arXiv:1208.1908},
year = {2013}
}