2012/07/23 by Soufiane Aazizi, Aazizi, Soufiane
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1207.5574
openalex publication_date 2012/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a simple technic to derive the Berry-Ess 'een bounds for the\nquadratic variation of the subfractional Brownian motion (subfBm). Our approach\nhas two main ingredients: (i) bounding from above the covariance of quadratic\nvariation of subfBm by the covariance of the quadratic variation of fractional\nBrownian motion (fBm); and (ii) using the existing results on fBm in\n citeBN08,NP09,N12. As a result, we obtain simple and direct proof to derive\nthe rate of convergence of quadratic variation of subfBm. In addition, we also\nimprove this rate of convergence to meet the one of fractional Brownian motion\nin citeN12.\n