Wave-length and amplitude for a stationary Gaussian process after a high maximum

1972 ◽  
Vol 23 (4) ◽  
pp. 293-326 ◽  
Author(s):  
Georg Lindgren
Keyword(s):  
Gaussian Process ◽  
Wave Length ◽  
Stationary Gaussian Process ◽  
High Maximum

Wave-length and amplitude in Gaussian noise

1972 ◽  
Vol 4 (1) ◽  
pp. 81-108 ◽  
Author(s):  
Georg Lindgren
Keyword(s):  
Gaussian Process ◽  
Density Function ◽  
Gaussian Noise ◽  
Covariance Function ◽  
Wave Length ◽  
Local Maximum ◽  
Stationary Gaussian Process ◽  
Numerical Examples ◽  
Vertical Distance

We give moment approximations to the density function of the wavelength, i. e., the time between “a randomly chosen” local maximum with height u and the following minimum in a stationary Gaussian process with a given covariance function. For certain processes we give similar approximations to the distribution of the amplitude, i. e., the vertical distance between the maximum and the minimum. Numerical examples and diagrams illustrate the results.

Wave-length and amplitude in Gaussian noise

1972 ◽  
Vol 4 (01) ◽  
pp. 81-108 ◽  
Author(s):  
Georg Lindgren
Keyword(s):  
Gaussian Process ◽  
Density Function ◽  
Gaussian Noise ◽  
Covariance Function ◽  
Wave Length ◽  
Local Maximum ◽  
Stationary Gaussian Process ◽  
Numerical Examples ◽  
Vertical Distance

We give moment approximations to the density function of the wavelength, i. e., the time between “a randomly chosen” local maximum with height u and the following minimum in a stationary Gaussian process with a given covariance function. For certain processes we give similar approximations to the distribution of the amplitude, i. e., the vertical distance between the maximum and the minimum. Numerical examples and diagrams illustrate the results.

Estimates on the distribution of the supremum of a stationary Gaussian process

1989 ◽  
Vol 41 (3) ◽  
pp. 279-286 ◽  
Author(s):  
Yu. V. Kozachenko ◽  
A. A. Pashko
Keyword(s):  
Gaussian Process ◽  
Stationary Gaussian Process

On the weak convergence of a class of estimators of the variance-time curve of a weakly stationary point process

1977 ◽  
Vol 14 (01) ◽  
pp. 114-126 ◽  
Author(s):  
A. M. Liebetrau
Keyword(s):  
Weak Convergence ◽  
Gaussian Process ◽  
Point Process ◽  
Stationary Point ◽  
Stationary Gaussian Process ◽  
Time Curve ◽  
Second Moment ◽  
Stationary Point Process ◽  
Class Of Estimators

The second-moment structure of an estimator V*(t) of the variance-time curve V(t) of a weakly stationary point process is obtained in the case where the process is Poisson. This result is used to establish the weak convergence of a class of estimators of the form Tβ (V*(tTα ) – V(tTα )), 0 < α < 1, to a non-stationary Gaussian process. Similar results are shown to hold when α = 0 and in the case where V(tTα ) is replaced by a suitable estimator.

The weak convergence of a class of estimators of the variance function of a two-dimensional Poisson process

1978 ◽  
Vol 15 (02) ◽  
pp. 433-439 ◽  
Author(s):  
A. M. Liebetrau
Keyword(s):  
Weak Convergence ◽  
Poisson Process ◽  
Gaussian Process ◽  
Higher Dimensions ◽  
Variance Function ◽  
Stationary Gaussian Process ◽  
Two Dimensional ◽  
Second Moment ◽  
Class Of Estimators

Results of a previous paper (Liebetrau (1977a)) are extended to higher dimensions. An estimator V∗(t 1, t 2) of the variance function V(t 1, t 2) of a two-dimensional process is defined, and its first- and second-moment structure is given assuming the process to be Poisson. Members of a class of estimators of the form where and for 0 < α i < 1, are shown to converge weakly to a non-stationary Gaussian process. Similar results hold when the t′i are taken to be constants, when V is replaced by a suitable estimator and when the dimensionality of the underlying Poisson process is greater than two.

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