On the modeling of linear system input stochastic processes with given accuracy and reliability

AbstractThe paper is devoted to the model construction for input stochastic processes of a time-invariant linear system with a real-valued square-integrable impulse response function. The processes are considered as Gaussian stochastic processes with discrete spectrum. The response on the system is supposed to be an output process. We obtain the conditions under which the constructed model approximates a Gaussian stochastic process with given accuracy and reliability in the Banach space{C([0,1])}, taking into account the response of the system. For this purpose, the methods and properties of square-Gaussian processes are used.

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Simulation of Gaussian stochastic processes

Random Operators and Stochastic Equations ◽

10.1515/156939703771378620 ◽

2003 ◽

Vol 11 (3) ◽

Author(s):

Yuri Kozachenko ◽

Iryna Rozora

Keyword(s):

Banach Space ◽

Stochastic Processes ◽

Gaussian Processes ◽

Gaussian Stochastic Processes

In this paper the Gaussian stochastic processes, represented in the form of series, are considered. The approximating models of the Gaussian processes with given reliability and accuracy in Banach space C

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An Upper Bound on the Failure Probability for Linear Structures

Journal of Applied Mechanics ◽

10.1115/1.3422921 ◽

1973 ◽

Vol 40 (1) ◽

pp. 181-185 ◽

Cited By ~ 3

Author(s):

L. H. Koopmans ◽

C. Qualls ◽

J. T. P. Yao

Keyword(s):

Stochastic Process ◽

Failure Probability ◽

Upper Bound ◽

Impulse Response Function ◽

Linear Structures ◽

Stochastic Response ◽

Gaussian Stochastic Process ◽

Exponential Bound ◽

Mean And Variance ◽

The Mean

This paper establishes a new upper bound on the failure probability of linear structures excited by an earthquake. From Drenick’s inequality max|y(t)| ≤ MN, where N2 = ∫h2, M2, = ∫x2, x(t) is a nonstationary Gaussian stochastic process representing the excitation of the earthquake, and y(t) is the stochastic response of the structure with impulse response function h(τ), we obtain an exponential bound computable in terms of the mean and variance of the energy M2. A numerical example is given.

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Über Linear Passive Transformationen Stochastischer Prozesse I

Zeitschrift für Naturforschung A ◽

10.1515/zna-1968-1002 ◽

1968 ◽

Vol 23 (10) ◽

pp. 1430-1438 ◽

Cited By ~ 3

Author(s):

J. Keller

Keyword(s):

Stochastic Process ◽

Stochastic Processes ◽

Mean Value ◽

Output Process ◽

Passive Systems ◽

Physical Systems ◽

General Properties ◽

Input And Output ◽

The Mean

The theory of linear passive systems, developed by KÖNIG and MEIXNER, is extended to the case where the input is not a well determined function of time but rather a stochastic process. In this case the answer of the system generally will also be a stochastic process. The input and output processes are connected by a linear passive transformation (LPT). Some examples are given of physical systems which may be described by LPT of stochastic processes. General properties of the mean value and the dispersion of the output process are derived.

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Sample continuity with probability one for the estimator of impulse response function

Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics ◽

10.17721/1812-5409.2020/3.10 ◽

2020 ◽

pp. 96-102

Author(s):

I. V. Rozora

Keyword(s):

Linear System ◽

Impulse Response ◽

Response Function ◽

Impulse Response Function ◽

Black Box ◽

Errors In Variables ◽

Stochastic Linear System ◽

Impulse Function ◽

Active Research ◽

Time Invariant

The problem of estimation of a stochastic linear system has been a matter of active research for the last years. One of the simplest models considers a ‘black box’ with some input and a certain output. The input may be single or multiple and there is the same choice for the output. This generates a great amount of models that can be considered. The sphere of applications of these models is very extensive, ranging from signal processing and automatic control to econometrics (errors-in-variables models). In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function. We assume that impulse function is square-integrable. Input signal is supposed to be Gaussian stationary stochastic process with known spectral density. A sample input–output crosscorrelogram is taken as an estimator of the response function. The conditions on sample continuousness with probability one for impulse response function are investigated.

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Conditional Simulation of No-Gaussian Stochastic Process Based on Neural Networks

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.479-481.1959 ◽

2012 ◽

Vol 479-481 ◽

pp. 1959-1962

Author(s):

Jin Hua Li ◽

Shui Sheng Chen ◽

Wei Bing Sheng

Keyword(s):

Neural Network ◽

Stochastic Processes ◽

Conditional Simulation ◽

Back Propagation ◽

Back Propagation Neural Network ◽

Generalized Regression Neural Network ◽

Ocean Engineering ◽

Gaussian Stochastic Process ◽

Non Gaussian ◽

Gaussian Stochastic Processes

In many fields such as wind engineering, ocean engineering, soil engineering and so on, it is obvious that the development of effective methods to generate sample functions of non-Gaussian stochastic processes and fields is of paramount significance for many systems subjected to non-Gaussian excitations. In this paper, neural network technique is proposed for the conditional simulation of non-Gaussian stochastic processes and fields. In machine learning of neural network, interpolation is employed to train finite non-Gaussian samples. As numerical examples, the conditional simulation of non-Gaussian fluctuating wind pressures is carried out through using back propagation neural network and generalized regression neural network respectively.

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Evaluations of absorption probabilities for the Wiener process on large intervals

Journal of Applied Probability ◽

10.1017/s0021900200047197 ◽

1980 ◽

Vol 17 (02) ◽

pp. 363-372 ◽

Cited By ~ 7

Author(s):

C. Park ◽

F. J. Schuurmann

Keyword(s):

Stochastic Processes ◽

Wiener Process ◽

Standard Wiener Process ◽

Computationally Efficient ◽

The Past ◽

Gaussian Stochastic Processes ◽

Absorption Probabilities

Let {W(t), 0≦t<∞} be the standard Wiener process. The computation schemes developed in the past are not computationally efficient for the absorption probabilities of the type P{sup0≦t≦T W(t) − f(t) ≧ 0} when either T is large or f(0) > 0 is small. This paper gives an efficient and accurate algorithm to compute such probabilities, and some applications to other Gaussian stochastic processes are discussed.

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Stochastic Processes with a Particular Type of Variograms

Research Letters in Signal Processing ◽

10.1155/2007/61579 ◽

2007 ◽

Vol 2007 ◽

pp. 1-5 ◽

Cited By ~ 1

Author(s):

Chunsheng Ma

Keyword(s):

Stochastic Process ◽

Brownian Motion ◽

Stochastic Processes ◽

Series Expansion ◽

Real Line ◽

Random Fields ◽

The Other ◽

Simple Construction ◽

The Real ◽

Line Form

This paper is concerned with a class of stochastic processes or random fields with second-order increments, whose variograms have a particular form, among which stochastic processes having orthogonal increments on the real line form an important subclass. A natural issue, how big this subclass is, has not been explicitly addressed in the literature. As a solution, this paper characterizes a stochastic process having orthogonal increments on the real line in terms of its variogram or its construction. Our findings are a little bit surprising: this subclass is big in terms of the variogram, and on the other hand, it is relatively “small” according to a simple construction. In particular, every such process with Gaussian increments can be simply constructed from Brownian motion. Using the characterizations we obtain a series expansion of the stochastic process with orthogonal increments.

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