Numerical Generation of Compound Random Processes with an Arbitrary Autocorrelation Function

2018 ◽  
Vol 17 (01) ◽  
pp. 1850001 ◽  
Author(s):  
Dima Bykhovsky ◽  
Tom Trigano
Keyword(s):  
Random Process ◽  
Autocorrelation Function ◽  
Analytical Study ◽  
Random Processes ◽  
The Other ◽  
Gaussian Random Process ◽  
Numerical Examples ◽  
Compound Process ◽  
Numerical Generation ◽  
Non Gaussian

The generation of non-Gaussian random processes with a given autocorrelation function (ACF) is addressed. The generation is based on a compound process with two components. Both components are solutions of appropriate stochastic differential equations (SDEs). One of the components is a Gaussian process and the other one is non-Gaussian with an exponential ACF. The analytical study shows that a compound combination of these processes may be used for the generation of a non-Gaussian random process with a required ACF. The results are verified by two numerical examples.

On the two sided barrier problem

1965 ◽  
Vol 2 (01) ◽  
pp. 79-87
Author(s):  
Masanobu Shinozuka
Keyword(s):  
Random Process ◽  
Ground Motion ◽  
Lower Bounds ◽  
Present Method ◽  
Structural Response ◽  
Random Processes ◽  
Upper And Lower Bounds ◽  
Numerical Examples ◽  
Long Run ◽  
Barrier Problem

Upper and lower bounds are given for the probability that a separable random process X(t) will take values outside the interval (— λ 1, λ 2) for 0 ≦ t ≦ T, where λ 1 and λ 2 are positive constants. The random process needs to be neither stationary, Gaussian nor purely random (white noise). In engineering applications, X(t) is usually a random process decaying with time at least in the long run such as the structural response to the acceleration of ground motion due to earthquake. Numerical examples show that the present method estimates the probability between the upper and lower bounds which are sufficiently close to be useful when the random processes decay with time.

Identification of Non-Gaussian Stochastic System

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Sung-man Park ◽  
O-shin Kwon ◽  
Jin-sung Kim ◽  
Jong-bok Lee ◽  
Hoon Heo
Keyword(s):  
Random Process ◽  
Random Noise ◽  
Stochastic Simulations ◽  
Kolmogorov Equation ◽  
Gaussian Random Process ◽  
System Parameters ◽  
Analysis Technique ◽  
Gaussian Analysis ◽  
Gaussian System ◽  
Non Gaussian

This paper proposes a method to identify non-Gaussian random noise in an unknown system through the use of a modified system identification (ID) technique in the stochastic domain, which is based on a recently developed Gaussian system ID. The non-Gaussian random process is approximated via an equivalent Gaussian approach. A modified Fokker–Planck–Kolmogorov equation based on a non-Gaussian analysis technique is adopted to utilize an effective Gaussian random process that represents an implied non-Gaussian random process. When a system under non-Gaussian random noise reveals stationary moment output, the system parameters can be extracted via symbolic computation. Monte Carlo stochastic simulations are conducted to reveal some approximate results, which are close to the actual values of the system parameters.

On the two sided barrier problem

1965 ◽  
Vol 2 (1) ◽  
pp. 79-87 ◽  
Author(s):  
Masanobu Shinozuka
Keyword(s):  
Random Process ◽  
Ground Motion ◽  
Lower Bounds ◽  
Present Method ◽  
Structural Response ◽  
Random Processes ◽  
Upper And Lower Bounds ◽  
Numerical Examples ◽  
Long Run ◽  
Barrier Problem

Upper and lower bounds are given for the probability that a separable random process X(t) will take values outside the interval (— λ1, λ2) for 0 ≦ t ≦ T, where λ1 and λ2 are positive constants.The random process needs to be neither stationary, Gaussian nor purely random (white noise).In engineering applications, X(t) is usually a random process decaying with time at least in the long run such as the structural response to the acceleration of ground motion due to earthquake.Numerical examples show that the present method estimates the probability between the upper and lower bounds which are sufficiently close to be useful when the random processes decay with time.

WAVELET ANALYSIS FOR RANDOM PROCESSES

2001 ◽  
Vol 16 (09) ◽  
pp. 583-588
Author(s):  
ZHIMING LI ◽  
QIN WANG ◽  
YUANFANG WU
Keyword(s):  
Wavelet Analysis ◽  
Random Process ◽  
Wavelet Transformation ◽  
Random Processes ◽  
The Other ◽  
Cascade Process ◽  
Apparent Increase ◽  
Scaling Index ◽  
Multiplicative Cascade

The role of wavelet transformation in the study of random processes is investigated. It is shown that wavelet transformation does not change the scaling index of random multiplicative cascade process. On the other hand, for pure random process, wavelet transformation is able to suppress the trivial fluctuations, coming from probability conservation, which will show an apparent increase in moments with the diminishing of bin size.

scholarly journals Duration Distribution and Up-crossings Rate of Generalized Hyperbolic Processes

2016 ◽  
Vol 36 (3) ◽  
Author(s):  
Moh’d T. Alodat ◽  
Khalid M. Aludaat
Keyword(s):  
Gaussian Process ◽  
Random Process ◽  
Alternative Model ◽  
Sea Surface ◽  
Surface Elevation ◽  
Gaussian Random Process ◽  
Duration Distribution ◽  
Non Gaussian

A Gaussian process is usually used to model the sea surface elevation in the oceanography. As the depth of the water decreases or the sea severity increases, the sea surface elevation departs from symmetry and Gaussianity. In this paper, a stationary non-Gaussian random process called the generalized hyperbolic process is used as an alternative model. The process generates a family of processes. We derive the rate of up-crossings for this process and the distribution of the height of the process. We also derive the duration distribution of an excursion for the generalized hyperbolic process.

Extreme values of the cyclostationary Gaussian random process

1993 ◽  
Vol 30 (01) ◽  
pp. 82-97 ◽  
Author(s):  
D. G. Konstant ◽  
V.I. Piterbarg
Keyword(s):  
Gaussian Process ◽  
Random Process ◽  
Gaussian Processes ◽  
Extreme Values ◽  
Random Processes ◽  
Mean Square ◽  
Gaussian Random Process ◽  
Covariance Functions ◽  
Limit Formula ◽  
Image Position

In this paper the class of cyclostationary Gaussian random processes is studied. Basic asymptotics are given for the class of Gaussian processes that are centered and differentiable in mean square. Then, under certain conditions on the non-degeneration of the centered cyclostationary Gaussian process with integrable covariance functions, the Gnedenko-type limit formula is established for and all x > 0.

Extreme values of the cyclostationary Gaussian random process

1993 ◽  
Vol 30 (1) ◽  
pp. 82-97 ◽  
Author(s):  
D. G. Konstant ◽  
V.I. Piterbarg
Keyword(s):  
Gaussian Process ◽  
Random Process ◽  
Gaussian Processes ◽  
Extreme Values ◽  
Random Processes ◽  
Mean Square ◽  
Gaussian Random Process ◽  
Covariance Functions ◽  
Limit Formula ◽  
Image Position

In this paper the class of cyclostationary Gaussian random processes is studied. Basic asymptotics are given for the class of Gaussian processes that are centered and differentiable in mean square. Then, under certain conditions on the non-degeneration of the centered cyclostationary Gaussian process with integrable covariance functions, the Gnedenko-type limit formula is established for and all x > 0.

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