Output distributions and covariance functions of certain non-linear transformations

• Main Author: Cheng, M.C.
• Format: Article
• Published: Taylor & Francis 1971
• Subjects: QA Mathematics
• Online Access: http://eprints.um.edu.my/24473/; https://doi.org/10.1080/00207177108932006

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.