Wiener--Ito integral representation in vector valued Gaussian stationary random fields

Peter Major

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arXiv · 1901.04084

Wiener--Ito integral representation in vector valued Gaussian stationary random fields

Peter Major

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Abstract

The subject of this work is the multivariate generalization of the theory of multiple Wiener--It\^o integrals. In the scalar valued case this theory was described in paper\cite{11}. Our proofs apply the technique of this work, but in the proof of some results new ideas were needed. The motivation for this study was a result in paper\cite{1} of Arcones where he formulated the multivariate version of a non-central limit theorem for non-linear functionals of Gaussian stationary random fields presented in paper\cite{6}. We found the proof in paper\cite{1} incomplete and wanted to give a full proof. We did it in paper\cite{13}, but in that proof we needed a detailed description of the properties of non-linear functionals of vector valued stationary Gaussian fields. Here we provide the foundation needed to carry out that proof. --More--(0%)

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Peter Major. 2019-01-13. Wiener--Ito integral representation in vector valued Gaussian stationary random fields. https://arxiv.org/abs/1901.04084

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