2019/01/13 by Péter Major, Major, Peter
Mathematics · Economics, Econometrics and Finance · #Probability and Statistical Research #Geometry and complex manifolds #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1901.04084
The subject of this work is the multivariate generalization of the theory of multiple Wiener--Itô integrals. In the scalar valued case this theory was described in paper\cite11. 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\cite1 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\cite6. We found the proof in paper\cite1 incomplete and wanted to give a full proof. We did it in paper\cite13, 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%)