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

TL;DR

This paper uses white noise analysis to establish limit theorems for nonlinear functionals of Volterra processes, including fractional Brownian motion, extending classical results and recent developments in stochastic analysis.

Contribution

It introduces new limit theorems for nonlinear functionals of Volterra processes using white noise analysis, broadening understanding of their asymptotic behavior.

Findings

Proves limit theorems for nonlinear functionals of Volterra processes.

Applies results specifically to fractional Brownian motion.

Connects classical and recent advances in stochastic process analysis.

Abstract

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.