Rational $q\times q$ Carath\'eodory Functions and Central Non-negative Hermitian Measures
Complex Variables
2015-12-18 v1 Probability
Abstract
We give an explicit representation of central measures corresponding to finite Toeplitz non-negative definite sequences of complex matrices. Such measures are intimately connected to central Carath\'eodory functions. This enables us to prove an explicit representation of the non-stochastic spectral measure of an arbitrary multivariate autoregressive stationary sequence in terms of the covariance sequence.
Keywords
Cite
@article{arxiv.1512.05560,
title = {Rational $q\times q$ Carath\'eodory Functions and Central Non-negative Hermitian Measures},
author = {Bernd Fritzsche and Bernd Kirstein and Conrad Mädler},
journal= {arXiv preprint arXiv:1512.05560},
year = {2015}
}