Limit theorems for nonlinear functionals of Volterra processes via white noise analysis

Details Limit theorems for nonlinear functionals of Volterra processes via white noise analysis Limit theorems for nonlinear functionals of Volterra processes via white noise analysis

2009-04-08

arxiv.org/abs/0904.1401v2

Bernoulli 2010, Vol. 16, No. 4, 1262-1293

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/10-BEJ258 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ258

By means of white noise analysis, we prove some limit theorems for nonlinear functionals of a given Volterra process. In particular, our results apply to fractional Brownian motion (fBm) and should be compared with the classical convergence results of the 1980s due to Breuer, Dobrushin, Giraitis, Major, Surgailis and Taqqu, as well as the recent advances concerning the construction of a L\'{e}vy area for fBm due to Coutin, Qian and Unterberger.

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