Limit theorems for functionals of Gaussian vectors

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

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