2020/11/11 by G. L. Feltes, Feltes, G. L., Sílvia R. C. Lopes +1
Economics, Econometrics and Finance · #54E99 #60G10 #62E10 #62H20 #62M10 #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.2011.06067
openalex publication_date 2020/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Long memory processes driven by Lévy noise with finite second-order moments have been well studied in the literature. They form a very rich class of processes presenting an autocovariance function which decays like a power function. Here, we study a class of Lévy process whose second-order moments are infinite, the so-called α-stable processes. Based on Samorodnitsky and Taqqu (2000), we construct an isometry that allows us to define stochastic integrals concerning the linear fractional stable motion using Riemann-Liouville fractional integrals. With this construction, follows naturally an integration by parts formula. We then present a family of stationary SαS processes with the property of long-range dependence, using a generalized measure to investigate its dependence structure. In the end, the law of large number's result for a time's sample of the process is shown as an application of the isometry and integration by parts formula.