Characterization of vector valued, Gaussian, stationary, Markov processes
type: Item
instance of: scholarly article
title: Characterization of vector valued, Gaussian, stationary, Markov processes
zbMATH Open document ID: 0641.60045
DOI: 10.1016/0167-7152(87)90053-8
published in: Statistics \& Probability Letters
publication date: 1987-01-01T00:00:00Z
review text: The characterization of \textit{J. L. Doob} [Stochastic processes. (1953; Zbl 0053.268)] of real-valued stationary Gaussian Markov processes is extended to the vector case. In this case, a deterministic component appears that consists of a system of harmonic oscillators while the random part is a collection of independent oscillator processes, modulo linear changes of coordinates.
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 4044862
zbMATH Keywords: Ornstein-Uhlenbeck process
zbMATH Keywords: Markov property characterization
zbMATH Keywords: stationary Gaussian Markov processes
zbMATH Keywords: harmonic oscillators
author: Henryk Gzyl
reviewed by: Donald A. Dawson
MaRDI profile type: Publication
full work available at URL: 0167-7152(87)90053-8
OpenAlex ID: W2009679391
cites work: Q5822308
cites work: Q3872705
cites work: Statistical Mechanics of Assemblies of Coupled Oscillators
cites work: An Alternative Approach to Canonical Forms of Matrices
cites work: Q3929641
cites work: Q3254327
description: scientific article; zbMATH DE number 4044862