stationary gaussian processes
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2021 ◽  
Vol 385 ◽  
pp. 114007
Author(s):  
Piyush Pandita ◽  
Panagiotis Tsilifis ◽  
Nimish M. Awalgaonkar ◽  
Ilias Bilionis ◽  
Jitesh Panchal

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2687
Author(s):  
Guo-Qiang Cai ◽  
Ronghua Huan ◽  
Weiqiu Zhu

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.


2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Michele Ancona ◽  
Thomas Letendre

Author(s):  
D. Zatula

Complex random variables and processes with a vanishing pseudo-correlation are called proper. There is a class of stationary proper complex random processes that have a stable correlation function. In the present article we consider real stationary Gaussian processes with a stable correlation function. It is shown that the trajectories of stationary Gaussian proper complex random processes with zero mean belong to the Orlich space generated by the function $U(x) = e^{x^2/2}-1$. Estimates are obtained for the distribution of semi-norms of sample functions of Gaussian proper complex random processes with a stable correlation function, defined on the compact $\mathbb{T} = [0,T]$, in Hölder spaces.


2020 ◽  
Vol 68 ◽  
pp. 5260-5275 ◽  
Author(s):  
Feng Yin ◽  
Lishuo Pan ◽  
Tianshi Chen ◽  
Sergios Theodoridis ◽  
Zhi-Quan Tom Luo ◽  
...  

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