2019/01/13 by Péter Major, Major, Peter
Environmental Science · Economics, Econometrics and Finance · #Hydrology and Drought Analysis #Financial Risk and Volatility Modeling #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1901.04086
Here I prove non-central limit theorems for non-linear functionals of vector\nvalued stationary random fields under appropriate conditions. They are the\nmultivariate versions of the results in paper cite2. Previously A. M. Arcones\nformulated a theorem in paper cite1 which can be considered as the\nmultivariate generalization of these results. But I found Arcones' discussion\nincomplete, and in my opinion to give a complete proof first a more profound\nfoundation of the theory of vector valued Gaussian stationary random fields has\nto be worked out. This was done in my paper cite4 which enabled me to adapt\nthe method in paper cite2 to the study of the vector valued case. Here I\nprove with its help the desired multivariate version of the results in\npaper cite2.\n