Output distributions and covariance functions of certain non-linear transformations

Three specific non-linear transformations of Gaussian stochastic processes occurring in signal detection and control theory are considered. The Gaussian stochastic processes are not necessarily stationary. The common feature of the transformed stochastic processes is that the determination of their...

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Main Author: Cheng, M.C.
Format: Article
Published: Taylor & Francis 1971
Subjects:
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author Cheng, M.C.
author_facet Cheng, M.C.
author_sort Cheng, M.C.
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description Three specific non-linear transformations of Gaussian stochastic processes occurring in signal detection and control theory are considered. The Gaussian stochastic processes are not necessarily stationary. The common feature of the transformed stochastic processes is that the determination of their covariance functions depends upon the evaluation of the orthant probability of four Gaussian variates over the respective correlation matrix. A method for evaluating this orthant probability, when the correlation matrix has certain specific forms, has recently been discussed by Cheng (1969). The application of this method yields closed-form expressions, in terms of tabulated functions, for the output probability distributions and covariance functions of the non-linear transformations investigated. © 1970 Taylor & Francis Group, LLC.
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spelling um.eprints-244732021-03-24T03:21:10Z http://eprints.um.edu.my/24473/ Output distributions and covariance functions of certain non-linear transformations Cheng, M.C. QA Mathematics Three specific non-linear transformations of Gaussian stochastic processes occurring in signal detection and control theory are considered. The Gaussian stochastic processes are not necessarily stationary. The common feature of the transformed stochastic processes is that the determination of their covariance functions depends upon the evaluation of the orthant probability of four Gaussian variates over the respective correlation matrix. A method for evaluating this orthant probability, when the correlation matrix has certain specific forms, has recently been discussed by Cheng (1969). The application of this method yields closed-form expressions, in terms of tabulated functions, for the output probability distributions and covariance functions of the non-linear transformations investigated. © 1970 Taylor & Francis Group, LLC. Taylor & Francis 1971 Article PeerReviewed Cheng, M.C. (1971) Output distributions and covariance functions of certain non-linear transformations. International Journal of Control, 13 (6). pp. 1065-1071. ISSN 0020-7179, DOI https://doi.org/10.1080/00207177108932006 <https://doi.org/10.1080/00207177108932006>. https://doi.org/10.1080/00207177108932006 doi:10.1080/00207177108932006
spellingShingle QA Mathematics
Cheng, M.C.
Output distributions and covariance functions of certain non-linear transformations
title Output distributions and covariance functions of certain non-linear transformations
title_full Output distributions and covariance functions of certain non-linear transformations
title_fullStr Output distributions and covariance functions of certain non-linear transformations
title_full_unstemmed Output distributions and covariance functions of certain non-linear transformations
title_short Output distributions and covariance functions of certain non-linear transformations
title_sort output distributions and covariance functions of certain non linear transformations
topic QA Mathematics
work_keys_str_mv AT chengmc outputdistributionsandcovariancefunctionsofcertainnonlineartransformations