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Frontiers of Mathematics in China

Front. Math. China    2017, Vol. 12 Issue (4) : 821-842     DOI: 10.1007/s11464-016-0620-1
Limit theorems for functionals of Gaussian vectors
Hongshuai DAI1, Guangjun SHEN2(), Lingtao KONG1
1. School of Statistics, Shandong University of Finance and Economics, Jinan 250014, China
2. Department of Mathematics, Anhui Normal University, Wuhu 241000, China
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Operator self-similar processes, as an extension of self-similar processes, have been studied extensively. In this work, we study limit theorems for functionals of Gaussian vectors. Under some conditions, we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process.

Keywords Gaussian vector      operator self-similar process      operator fractional Brownian motion      scaling limit     
Corresponding Authors: Guangjun SHEN   
Issue Date: 06 July 2017
 Cite this article:   
Hongshuai DAI,Guangjun SHEN,Lingtao KONG. Limit theorems for functionals of Gaussian vectors[J]. Front. Math. China, 2017, 12(4): 821-842.
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Hongshuai DAI
Guangjun SHEN
Lingtao KONG
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