2020/05/23 by Ehsan Azmoodeh, Azmoodeh, Ehsan, Yuliya Mishura +3 · 1 citation
Economics, Econometrics and Finance · #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.2005.11602
openalex publication_date 2020/05/23 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The present paper investigates the effects of tempering the power law kernel\nof moving average representation of a fractional Brownian motion (fBm) on some\nlocal and global properties of this Gaussian stochastic process. Tempered\nfractional Brownian motion (TFBM) and tempered fractional Brownian motion of\nthe second kind (TFBMII) are the processes that are considered in order to\ninvestigate the role of tempering. Tempering does not change the local\nproperties of fBm including the sample paths and p-variation, but it has a\nstrong impact on the Breuer-Major theorem, asymptotic behavior of the 3rd and\n4th cumulants of fBm and the optimal fourth moment theorem.\n