Multiple stochastic fractional integrals: A transfer principle for multiple stochastic fractional integrals
type: Item
instance of: scholarly article
title: Multiple stochastic fractional integrals: A transfer principle for multiple stochastic fractional integrals
zbMATH Open document ID: 1020.60050
author: Constantin Tudor
author: Víctor Pérez-Abreu
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 2003-09-24T00:00:00Z
review text: The single Wiener integral representation of fractional Brownian motion \(B^H_t = \int K(t,s) dW_s\) using a deterministic two-parameter fractional kernel \(K\) is extended to a multiple Wiener integral representation of the fractional multiple stochastic integrals of \textit{A. Dasgupta} and \textit{G. Kallianpur} [Probab. Theory Relat. Fields 115, 505-525 (1999; Zbl 0948.60022)] and \textit{T. E. Duncan, Y. Hu} and \textit{B. Pasik-Duncan} [SIAM J. Control Optimization 38, 582-612 (2000; Zbl 0947.60061)], using a continuous fractional mapping on \(L^2([0,T]^n)\). These integrals are then related to multiple fractional Stratonovich integrals via a Hu-Meyer type formula. A fractional anticipating integral is defined through chaos decompositions, and a related anticipating affine equation is solved. Finally, a strong law of large numbers is formulated for the fractional Brownian motion.
reviewed by: Nicolas Privault
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 1933102
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: multiple fractional integrals
zbMATH Keywords: chaos decomposition
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1933102