Spectral Theorems of Multidimensional Dyadic Stationary Process and its One-sided Dyadic Moving Average Representation

摘要

Two spectral representations of the multidimensional dyadic stationary process and its correlation matrix are given, and the following is obtained: An n-dimensional dyadic stationary process ahs a representation as a one-sided dyadic moving average if and only if the process has a spectral density matrix with the constant rank m, a. e. [Lebes- gue measure].