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Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter $$H \in (0,\frac {1}{2})$$. (English) Zbl 1083.60027
This article is devoted to the construction of the extended stochastic integral with respect to the fractional Brownian motion. Using the duality with the stochastic derivative the authors construct the integral with the help of integration by part formula on the Wiener space and establish its properties for the wide set of Hurst parameters. The Itô and Tanaka formulas also are presented. For the Itô formula the authors use the localization arguments in order to avoid the moment restrictions. The comparison with symmetric integral with respect to the fractional Brownian motion is given.

##### MSC:
 60G15 Gaussian processes 60H05 Stochastic integrals 60H07 Stochastic calculus of variations and the Malliavin calculus
##### Keywords:
extended stochastic integral; symmetric integral
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