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Pré-Publication, Document De Travail Année : 2019

Skorohod and rough integration with respect to the non-commutative fractional Brownian motion

Résumé

We pursue our investigations, initiated in [8], about stochastic integration with respect to the non-commutative fractional Brownian motion (NC-fBm). Our main objective in this paper is to compare the pathwise constructions of [8] with a Skorohod-type interpretation of the integral. As a first step, we provide details on the basic tools and properties associated with non-commutative Malliavin calculus, by mimicking the presentation of Nualart's celebrated treatise [14]. Then we check that, just as in the classical (commutative) situation, Skorohod integration can indeed be considered in the presence of the NC-fBm, at least for a Hurst index H > 1 4. This finally puts us in a position to state and prove the desired comparison result, which can be regarded as an Itô-Stratonovich correction formula for the NC-fBm.
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Dates et versions

hal-02286188 , version 1 (13-09-2019)
hal-02286188 , version 2 (01-12-2020)

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Aurélien Deya, René Schott. Skorohod and rough integration with respect to the non-commutative fractional Brownian motion. 2019. ⟨hal-02286188v1⟩
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