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Stochastic integration with respect to fractional Brownian motion. (English) Zbl 1016.60043

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.

MSC:

60G15 Gaussian processes
60H05 Stochastic integrals
60J65 Brownian motion
60F25 \(L^p\)-limit theorems
60H07 Stochastic calculus of variations and the Malliavin calculus
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