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.

scholarly journals Asymptotics of Maxima of Strongly Dependent Gaussian Processes

2012 ◽  
Vol 49 (04) ◽  
pp. 1106-1118 ◽  
Author(s):  
Zhongquan Tan ◽  
Enkelejd Hashorva ◽  
Zuoxiang Peng
Keyword(s):  
Correlation Function ◽  
Long Range ◽  
Gaussian Processes ◽  
Limit Distribution ◽  
Strong Dependence ◽  
Dependence Conditions ◽  
Stationary Gaussian Processes

Let {Xn(t),t∈[0,∞)},n∈ℕ, be standard stationary Gaussian processes. The limit distribution oft∈[0,T(n)]|Xn(t)| is established asrn(t), the correlation function of {Xn(t),t∈[0,∞)},n∈ℕ, which satisfies the local and long-range strong dependence conditions, extending the results obtained in Seleznjev (1991).

scholarly journals Asymptotic distribution for the sum and maximum of Gaussian processes

2000 ◽  
Vol 37 (04) ◽  
pp. 958-971 ◽  
Author(s):  
W. P. McCormick ◽  
Y. Qi
Keyword(s):  
Correlation Function ◽  
Asymptotic Distribution ◽  
Gaussian Processes ◽  
Random Variables ◽  
Stationary Sequence ◽  
Asymptotic Independence ◽  
Standard Normal

Previous work on the joint asymptotic distribution of the sum and maxima of Gaussian processes is extended here. In particular, it is shown that for a stationary sequence of standard normal random variables with correlation function r, the condition r(n)ln n = o(1) as n → ∞ suffices to establish the asymptotic independence of the sum and maximum.

scholarly journals Asymptotics of Maxima of Strongly Dependent Gaussian Processes

2012 ◽  
Vol 49 (4) ◽  
pp. 1106-1118 ◽  
Author(s):  
Zhongquan Tan ◽  
Enkelejd Hashorva ◽  
Zuoxiang Peng
Keyword(s):  
Correlation Function ◽  
Long Range ◽  
Gaussian Processes ◽  
Limit Distribution ◽  
Strong Dependence ◽  
Dependence Conditions ◽  
Stationary Gaussian Processes

Let {Xn(t), t∈[0,∞)}, n∈ℕ, be standard stationary Gaussian processes. The limit distribution of t∈[0,T(n)]|Xn(t)| is established as rn(t), the correlation function of {Xn(t), t∈[0,∞)}, n∈ℕ, which satisfies the local and long-range strong dependence conditions, extending the results obtained in Seleznjev (1991).

scholarly journals Asymptotic distribution for the sum and maximum of Gaussian processes

2000 ◽  
Vol 37 (4) ◽  
pp. 958-971 ◽  
Author(s):  
W. P. McCormick ◽  
Y. Qi
Keyword(s):  
Correlation Function ◽  
Asymptotic Distribution ◽  
Gaussian Processes ◽  
Random Variables ◽  
Stationary Sequence ◽  
Asymptotic Independence ◽  
Standard Normal

Previous work on the joint asymptotic distribution of the sum and maxima of Gaussian processes is extended here. In particular, it is shown that for a stationary sequence of standard normal random variables with correlation function r, the condition r(n)ln n = o(1) as n → ∞ suffices to establish the asymptotic independence of the sum and maximum.

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.

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.

MIXED FRACTIONAL DIFFERENTIATION OPERATORS IN HÖLDER SPACES DEFINED BY USUAL HÖLDER CONDITION

2019 ◽  
Author(s):  
T. Mamatov ◽  
R. Sabirova ◽  
D. Barakaev
Keyword(s):  
Fractional Derivative ◽  
Fractional Differentiation ◽  
Hölder Condition ◽  
Hölder Spaces ◽  
Main Interest ◽  
Hölder Class ◽  
Holder Class ◽  
Function Of Two Variables ◽  
Holder Spaces

We study mixed fractional derivative in Marchaud form of function of two variables in Hölder spaces of different orders in each variables. The main interest being in the evaluation of the latter for the mixed fractional derivative in the cases Hölder class defined by usual Hölder condition

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