2016/12/31 by Benjamin Arras, Arras, Benjamin · 1 citation
Economics, Econometrics and Finance · #60G12 #60G18 #60G22 #60H05 #60H07 #60H40 #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1701.00129
openalex publication_date 2016/12/31 · openalex created_date 2017/01/13 · openalex updated_date 2026/07/28
In this paper, we combine Hida distribution theory and Sobolev-Watanabe-Kree spaces in order to study finely the link between forward integrals obtained by regularization and Wick-Itô integrals with respect to fractional Brownian motion and the Rosenblatt process. The new methodology developed in this paper allows to retrieve results for fractional Brownian motion and to obtain new results regarding the Rosenblatt process. In particular, an Itô formula for functionals of the Rosenblatt process is obtained which holds in the space of square-integrable random variables.