Carmona, Philippe; Coutin, Laure; Montseny, Gérard Stochastic integration with respect to fractional Brownian motion. (English) Zbl 1016.60043 Ann. Inst. Henri Poincaré, Probab. Stat. 39, No. 1, 27-68 (2003). For every value of the Hurst index \(H\in (0,1)\), this paper defines a stochastic integral with respect to fractional Brownian motion of index \(H\) by approximating fractional Brownian motion. For \(H>1/6\), an Itô’s change of variables formula is established which is more precise than Privault’s Itô formula (1998) (established for every \(H>0\)), since it only involves anticipating integrals with respect to a driving Brownian motion. Reviewer: Yuhu Feng (Shanghai) Cited in 2 ReviewsCited in 52 Documents MSC: 60G15 Gaussian processes 60H05 Stochastic integrals 60J65 Brownian motion 60F25 \(L^p\)-limit theorems 60H07 Stochastic calculus of variations and the Malliavin calculus Keywords:Gaussian process; stochastic integral; Malliavin calculus; fractional integration PDFBibTeX XMLCite \textit{P. Carmona} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 39, No. 1, 27--68 (2003; Zbl 1016.60043) Full Text: DOI Numdam EuDML