Approximation to two independent Gaussian processes from a unique Lévy process and applications

Jun Wang, Xianmei Song, Guangjun Shen and Xiuwei Yin

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 21, 5220-5234

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.

Date: 2020
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DOI: 10.1080/03610926.2019.1615095

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