Limit theorems for functionals of Gaussian vectors

doi:10.1007/s11464-016-0620-1

Front. Math. China

2017, Vol. 12

Issue (4) : 821-842 https://doi.org/10.1007/s11464-016-0620-1

RESEARCH ARTICLE

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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Abstract

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 Author(s): 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.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0620-1
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I4/821

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