Topic
Gaussian process
About: Gaussian process is a research topic. Over the lifetime, 18944 publications have been published within this topic receiving 486645 citations. The topic is also known as: Gaussian stochastic process.
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TL;DR: In this article, the geometry of random vibration problems in the space of standard normal random variables obtained from discretization of the input process is investigated and an approximate method for their solution is presented.
215 citations
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TL;DR: Based on these examples, it was shown that the proposed algorithm is more robust and general than the commonly used spectral representation method.
214 citations
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TL;DR: In this paper, the form of the asymptotic distribution of Z(t) is given for all a. The results of this work depend heavily upon some of the results involving upcrossings given in [7], provided appropriate but obvious modifications are made.
Abstract: and their behavior as t -> 00. In §2, the form of the asymptotic distribution of Z(t) is given for all a. This generalizes the result of [6] wherein a = 1, and the result of Cramer [4] and Volkonski and Rozanov [9], wherein a = 2. In §3, the almost sure asymptotic behaviour of Z(t) is investigated for all a. For the case a = 2, the result extends that of Shur [8]. The results of this work depend heavily upon some of the results involving upcrossings given in [7]. They are valid for smallest as well as for largest values, provided appropriate but obvious modifications are made.
214 citations
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TL;DR: Expressions for multivariate Rayleigh and exponential probability density functions (PDFs) generated from correlated Gaussian random variables can serve as a useful tool in the performance analysis of digital modulation over correlated Rayleigh-fading channels using diversity combining.
Abstract: In this paper, expressions for multivariate Rayleigh and exponential probability density functions (PDFs) generated from correlated Gaussian random variables are presented. We first obtain a general integral form of the PDFs, and then study the case when the complex Gaussian generating vector is circular. We consider two specific circular cases: the exchangeable case when the variates are evenly correlated, and the exponentially correlated case. Expressions for the multivariate PDF in these cases are obtained in integral form as well as in the form of a series of products of univariate PDFs. We also derive a general expression for the multivariate exponential characteristic function (CF) in terms of determinants. In the exchangeable and exponentially correlated cases, CF expressions are obtained in the form of a series of products of univariate gamma CFs. The CF of the sum of exponential variates in these cases is obtained in closed form. Finally, the bivariate case is presented mentioning its main features. While the integral forms of the multivariate PDFs provide a general analytical framework, the series and determinant expressions for the exponential CFs and the series expressions for the PDFs can serve as a useful tool in the performance analysis of digital modulation over correlated Rayleigh-fading channels using diversity combining.
214 citations
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213 citations