Approximate spectral models of random processes with periodic properties

2019 ◽  
Vol 34 (6) ◽  
pp. 353-360
Author(s):  
Alisa M. Medvyatskaya ◽  
Vasily A. Ogorodnikov
Keyword(s):  
Gaussian Processes ◽  
Spectral Representation ◽  
Random Processes ◽  
Spectral Models ◽  
Periodically Correlated Random Processes ◽  
Stationary Gaussian Processes ◽  
Spectral Representations

Abstract We consider approaches to simulation of periodically correlated random processes based on the nonstandard spectral representation of the process with parameters periodically varying in time and also on spectral representations using the vector stationary Gaussian processes.

scholarly journals Estimates for the distribution of Hölder semi-norms of real stationary Gaussian processes with a stable correlation function

2020 ◽  
pp. 25-30
Author(s):  
D. Zatula
Keyword(s):  
Correlation Function ◽  
Present Article ◽  
Gaussian Processes ◽  
Random Variables ◽  
Random Processes ◽  
Hölder Spaces ◽  
Stationary Gaussian Processes ◽  
Holder Spaces

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.

Second Order and Gaussian Fields

2006 ◽  
Author(s):  
Ulf Grenander ◽  
Michael I. Miller
Keyword(s):  
Gaussian Processes ◽  
Differential Operators ◽  
Random Processes ◽  
Second Order ◽  
Gaussian Fields ◽  
Orthogonal Expansions ◽  
Finite Graphs ◽  
The World ◽  
Spectral Representations ◽  
The Continuum

This chapter studies second order and Gaussian fields on the background spaces which are the continuum limits of the finite graphs. For this random processes in Hilbert spaces are examined. Orthogonal expansions such as Karhunen–Loeve are examined, with spectral representations of the processes established. Gaussian processes induced by differential operators representing physical processes in the world are studied.

On the Distribution of Rises and Falls in a Continuous Random Process

1965 ◽  
Vol 87 (2) ◽  
pp. 398-404 ◽  
Author(s):  
J. R. Rice ◽  
F. P. Beer
Keyword(s):  
Experimental Data ◽  
Continuous Function ◽  
Random Process ◽  
General Result ◽  
Gaussian Processes ◽  
Random Processes ◽  
Statistical Information ◽  
Approximate Methods ◽  
Special Cases ◽  
Stationary Gaussian Processes

This paper is concerned with the statistics of the height of rise and full for continuous random processes. In particular, approximate methods are given for determining the probability density of the increment in a random continuous function as the function passes from one extremum to the next. Application of the general result is made to the case of processes with a Gaussian distribution. Numerical results are given for four special cases of stationary Gaussian processes. Computed results are found to agree well with available experimental data. The knowledge of such statistical information is of use in studies dealing with fatigue under random loadings.

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