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arXiv · 1909.06270

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

Aurélien Deya·René Schott
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Abstract

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 It{ô}-Stratonovich correction formula for the NC-fBm.

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Aurélien Deya, René Schott. 2020-12-01. Skorohod and rough integration with respect to the non-commutative fractional Brownian motion. https://arxiv.org/abs/1909.06270

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