标题：Limit theorems for functionals of two independent Gaussian processes
作者：Song, Jian; Xu, Fangjun; Yu, Qian
作者机构：[Song, Jian] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.; [Xu, Fangjun] East China Normal Univ, Sch Stat, MOE, Key Lab Adv The 更多
通讯作者：Xu, FJ;Xu, Fangjun
通讯作者地址：[Xu, FJ]East China Normal Univ, Sch Stat, MOE, Key Lab Adv Theory & Applicat Stat & Data Sci, Shanghai 200062, Peoples R China.
来源：STOCHASTIC PROCESSES AND THEIR APPLICATIONS
关键词：Limit theorem; Gaussian processes; Method of moments; Chaining argument;; Pairing technique
摘要：Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and bi-fractional Brownian motion. A new and interesting phenomenon is that, in comparison with the results for fractional Brownian motion, extra randomness appears in the limiting distributions for Gaussian processes with nonstationary increments, say sub-fractional Brownian motion and bi-fractional Brownian. The results are obtained based on the method of moments, in which Fourier analysis, the chaining argument introduced in  and a pairing technique are employed. (C) 2018 Elsevier B.V. All rights reserved.