Approximation to two independent Gaussian processes from a unique Lévy process and applications. Issue 21 (1st November 2020)

• Record Type: Journal Article
• Authors: Wang, Jun; Song, Xianmei; Shen, Guangjun; Yin, Xiuwei
• Is Part Of: Communications in statistics. Volume 49:Issue 21(2020)
• Page Start: 5220
• Page End: 5234
• Publication Date: 2020-11-01
• Subjects: Weak convergence -- self-similar -- fractional Brownian motion -- sub-fractional Brownian motion -- bifractional Brownian motion -- lévy process; 60F17 -- 60G15 -- 60G18; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2019.1615095
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: In this article, we construct two families of processes, from a unique Lévy process, the finite dimensional distributions of which converge in law towards the finite dimensional distributions of the two independent Gaussian processes. As applications of this result, we obtain families of processes that converge in law towards fractional Brownian motion, sub-fractional Brownian motion and bifractional Brownian motion, respectively.