Generation of Two Correlated Stationary Gaussian Processes

Since correlated stochastic processes are often presented in practical problems, feasible methods to model and generate correlated processes appropriately are needed for analysis and simulation. The present paper systematically presents three methods to generate two correlated stationary Gaussian pr...

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Autores principales:	Guo-Qiang Cai, Ronghua Huan, Weiqiu Zhu
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	correlated stochastic processes liner filters series expansion random amplitudes random phases simulations Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/4fdbc0d53727465bab8941fdfae26876
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spelling	oai:doaj.org-article:4fdbc0d53727465bab8941fdfae268762021-11-11T18:15:15ZGeneration of Two Correlated Stationary Gaussian Processes10.3390/math92126872227-7390https://doaj.org/article/4fdbc0d53727465bab8941fdfae268762021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2687https://doaj.org/toc/2227-7390Since correlated stochastic processes are often presented in practical problems, feasible methods to model and generate correlated processes appropriately are needed for analysis and simulation. The present paper systematically presents three methods to generate two correlated stationary Gaussian processes. They are (1) the method of linear filters, (2) the method of series expansion with random amplitudes, and (3) the method of series expansion with random phases. All three methods intend to match the power spectral density for each process but use information of different levels of correlation. The advantages and disadvantages of each method are discussed.Guo-Qiang CaiRonghua HuanWeiqiu ZhuMDPI AGarticlecorrelated stochastic processesliner filtersseries expansionrandom amplitudesrandom phasessimulationsMathematicsQA1-939ENMathematics, Vol 9, Iss 2687, p 2687 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	correlated stochastic processes liner filters series expansion random amplitudes random phases simulations Mathematics QA1-939
spellingShingle	correlated stochastic processes liner filters series expansion random amplitudes random phases simulations Mathematics QA1-939 Guo-Qiang Cai Ronghua Huan Weiqiu Zhu Generation of Two Correlated Stationary Gaussian Processes
description	Since correlated stochastic processes are often presented in practical problems, feasible methods to model and generate correlated processes appropriately are needed for analysis and simulation. The present paper systematically presents three methods to generate two correlated stationary Gaussian processes. They are (1) the method of linear filters, (2) the method of series expansion with random amplitudes, and (3) the method of series expansion with random phases. All three methods intend to match the power spectral density for each process but use information of different levels of correlation. The advantages and disadvantages of each method are discussed.
format	article
author	Guo-Qiang Cai Ronghua Huan Weiqiu Zhu
author_facet	Guo-Qiang Cai Ronghua Huan Weiqiu Zhu
author_sort	Guo-Qiang Cai
title	Generation of Two Correlated Stationary Gaussian Processes
title_short	Generation of Two Correlated Stationary Gaussian Processes
title_full	Generation of Two Correlated Stationary Gaussian Processes
title_fullStr	Generation of Two Correlated Stationary Gaussian Processes
title_full_unstemmed	Generation of Two Correlated Stationary Gaussian Processes
title_sort	generation of two correlated stationary gaussian processes
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/4fdbc0d53727465bab8941fdfae26876
work_keys_str_mv	AT guoqiangcai generationoftwocorrelatedstationarygaussianprocesses AT ronghuahuan generationoftwocorrelatedstationarygaussianprocesses AT weiqiuzhu generationoftwocorrelatedstationarygaussianprocesses
_version_	1718431882345971712

Generation of Two Correlated Stationary Gaussian Processes

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