Approximation to two independent Gaussian processes from a unique Lévy process and applications |
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| Authors: | Jun Wang Xianmei Song Xiuwei Yin |
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| Institution: | 1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, China;2. School of Mathematics and Finance, Chuzhou University, Chuzhou, China;3. Department of Mathematics, Anhui Normal University, Wuhu, China |
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| Abstract: | AbstractIn 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. |
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| Keywords: | Weak convergence self-similar fractional Brownian motion sub-fractional Brownian motion bifractional Brownian motion lévy process |
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