2019/09/13 by Aurélien Deya, Deya, Aurélien, René Schott +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Mathematics #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Operator Algebras (math.OA) #Probability (math.PR) #Random Matrices and Applications #Statistical Mechanics and Entropy #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1909.06270
openalex publication_date 2019/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.