Chaos decomposition of multiple fractional integrals and applications
The paper provides a chaos decomposition of the multiple Wiener integrals with respect to fractional Brownian motion with index \(H\in]\frac{1}{2},1[\). These multiple integrals are \(\text{ L}^{2}\)-functionals of fractional Brownian motion. Denote by \({\overline G}_{p}\) the \(p\)th homogeneous chaos. The authors identify the elements in \({\overline G}_{m}\), \(m< p\), which correspond to a multiple fractional integral of order \(p\). Also, conversely, the chaos components are expressed in terms of multiple fractional integrals of successively lower orders. An extension of a strong law [see also \textit{E. G. Gladyshev}, Theory Probab. Appl. 6, 52-61 (1961); translation from Teor. Veroyatn. Primen. 6, 57-66 (1961; Zbl 0107.12601)] for fractional Brownian motion is given as application.
scientific article; zbMATH DE number 1416526