Chaos decomposition of multiple fractional integrals and applications
type: Item
instance of: scholarly article
title: Chaos decomposition of multiple fractional integrals and applications
zbMATH Open document ID: 0952.60043
author: Gopinath Kallianpur
author: Amites Dasgupta
publication date: 2001-01-02T00:00:00Z
review text: 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.
reviewed by: Mihai Gradinaru
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 1416526
zbMATH Keywords: multiple stochastic integral
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: chaos expansion
zbMATH Keywords: tensor products
MaRDI profile type: Publication
full work available at URL: s004400050248
OpenAlex ID: W1998106040
DOI: 10.1007/S004400050248
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1416526