scholarly journals Some Applications of Higher Moments of the Linear Gaussian White Noise Process

2017 ◽  
Vol 08 (12) ◽  
pp. 1918-1938 ◽  
Author(s):  
I. S. Iwueze ◽  
C. O. Arimie ◽  
H. C. Iwu ◽  
E. Onyemachi
Keyword(s):  
White Noise ◽  
Gaussian White Noise ◽  
Higher Moments ◽  
White Noise Process ◽  
Noise Process ◽  
Gaussian White Noise Process

The exact bispectra for bilinear realizable processes with hermite degree 2

1991 ◽  
Vol 23 (04) ◽  
pp. 798-808 ◽  
Author(s):  
György Terdik ◽  
Laurie Meaux
Keyword(s):  
White Noise ◽  
Discrete Time ◽  
Hermite Polynomial ◽  
Transfer Functions ◽  
Gaussian White Noise ◽  
Second Order ◽  
Bilinear Model ◽  
White Noise Process ◽  
Noise Process ◽  
Gaussian White Noise Process

This paper deals with the stationary bilinear model with Hermite degree 2 in discrete time which is built up by the first- and second-order Hermite polynomial of a Gaussian white noise process. The exact spectrum and bispectrum is constructed in terms of the transfer functions of the model.

The exact bispectra for bilinear realizable processes with hermite degree 2

1991 ◽  
Vol 23 (4) ◽  
pp. 798-808 ◽  
Author(s):  
György Terdik ◽  
Laurie Meaux
Keyword(s):  
White Noise ◽  
Discrete Time ◽  
Hermite Polynomial ◽  
Transfer Functions ◽  
Gaussian White Noise ◽  
Second Order ◽  
Bilinear Model ◽  
White Noise Process ◽  
Noise Process ◽  
Gaussian White Noise Process

This paper deals with the stationary bilinear model with Hermite degree 2 in discrete time which is built up by the first- and second-order Hermite polynomial of a Gaussian white noise process. The exact spectrum and bispectrum is constructed in terms of the transfer functions of the model.

Active Control of Along-Wind Response of a Tall Building with AMD Using LQR Controller

2014 ◽  
Vol 490-491 ◽  
pp. 1063-1067 ◽  
Author(s):  
Young Moon Kim ◽  
Ki Pyo You ◽  
Jang Youl You
Keyword(s):  
White Noise ◽  
Gaussian White Noise ◽  
Wind Load ◽  
Tall Building ◽  
White Noise Process ◽  
Noise Process ◽  
Gaussian White Noise Process ◽  
Wind Response ◽  
Wind Vibration ◽  
Lqr Controller

Most of modern tall buildings using lighter construction materials are more flexible so could be excessive wind-induced vibrations resulting in occupant discomfort and structural unsafety. The optimal control technique for reducing along-wind vibration of a tall building based on the linear quadratic regulator (LQR) is presented in this work. Actively controlled reduced along-wind vibration response is obtained from the tall building installed in an active mass damper (AMD) with a LQR controller. Fluctuating along-wind load is generated using numerical simulation method, which can formulate a stationary Gaussian white noise process. Simulating wind load in the time domain using known spectra data of fluctuating along-wind load is particularly useful for estimation of windinduced vibration which is more or less narrow banded process such as a along-wind response of a tall building. In this work, fluctuating along-wind load acting on a tall building treated as a stationary Gaussian white noise process is simulated numerically using the along-wind load spectra proposed by G. Solari in1992. And using this simulated along-wind load estimated the reduced along-wind vibration response of a tall building installed in an AMD with a LQR controller.

scholarly journals On the Basel Liquidity Formula for Elliptical Distributions

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 92
Author(s):  
Janine Balter ◽  
Alexander McNeil
Keyword(s):  
Risk Factor ◽  
White Noise ◽  
Gaussian White Noise ◽  
General Assumption ◽  
Elliptical Distributions ◽  
Risk Capital ◽  
White Noise Process ◽  
Gaussian White Noise Process ◽  
Loss Distributions ◽  
Symmetric Loss

A justification of the Basel liquidity formula for risk capital in the trading book is given under the assumption that market risk-factor changes form a Gaussian white noise process over 10-day time steps and changes to P&L (profit-and-loss) are linear in the risk-factor changes. A generalization of the formula is derived under the more general assumption that risk-factor changes are multivariate elliptical. It is shown that the Basel formula tends to be conservative when the elliptical distributions are from the heavier-tailed generalized hyperbolic family. As a by-product of the analysis, a Fourier approach to calculating expected shortfall for general symmetric loss distributions is developed.

Driver Steering Control and a New Perspective on Car Handling Qualities

2005 ◽  
Vol 219 (10) ◽  
pp. 1041-1051 ◽  
Author(s):  
R S Sharp
Keyword(s):  
White Noise ◽  
Gaussian White Noise ◽  
Design Parameters ◽  
Steering Wheel ◽  
Steering Control ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Handling Qualities ◽  
Gaussian White Noise Process ◽  
Low Pass

The article is about steering control of cars by drivers, concentrating on following the lateral profile of the roadway, which is presumed visible ahead of the car. It builds on previously published work, in which it was shown how the driver's preview of the roadway can be combined with the linear dynamics of a simple car to yield a problem of discrete-time optimal-linear-control-theory form. In that work, it was shown how an optimal ‘driver’ of a linear car can convert the path preview sample values, modelled as deriving from a Gaussian white-noise process, into steering wheel displacement commands to cause the car to follow the previewed path with an attractive compromise between precision and ease. Recognizing that real roadway excitation is not so rich in high frequencies as white-noise, a low-pass filter is added to the system. The white-noise sample values are filtered before being seen by the driver. Numerical results are used to show that the optimal preview control is unaltered by the inclusion of the low-pass filter, whereas the feedback control is affected diminishingly as the preview increases. Then, using the established theoretical basis, new results are generated to show time-invariant optimal preview controls for cars and drivers with different layouts and priorities. Tight and loose controls, representing different balances between tracking accuracy and control effort, are calculated and illustrated through simulation. A new performance criterion with handling qualities implications is set up, involving the minimization of the preview distance required. The sensitivities of this distance to variations in the car design parameters are calculated. The influence of additional rear wheel steering is studied from the viewpoint of the preview distance required and the form of the optimal preview gain sequence. Path-following simulations are used to illustrate relatively high-authority and relatively low-authority control strategies, showing manoeuvring well in advance of a turn under appropriate circumstances. The results yield new insights into driver steering control behaviour and vehicle design optimization. The article concludes with a discussion of research in progress aimed at a further improved understanding of how drivers control their vehicles.

scholarly journals Empirical White Noise Processes and the Subjective Probabilistic Approaches

2019 ◽  
Vol 48 (1) ◽  
pp. 19-30
Author(s):  
András Rövid ◽  
László Palkovics ◽  
Péter Várlaki
Keyword(s):  
White Noise ◽  
Random Number ◽  
White Noise Process ◽  
Random Number Generators ◽  
Noise Process ◽  
Complementary Approach ◽  
Fuzzy Random

The paper discusses the identification of the empirical white noise processes generated by deterministic numerical algorithms.The introduced fuzzy-random complementary approach can identify the inner hidden correlational patterns of the empirical white noise process if the process has a real hidden structure of this kind. We have shown how the characteristics of auto-correlated white noise processes change as the order of autocorrelation increases. Although in this paper we rely on random number generators to get approximate white noise processes, in our upcoming research we are planning to turn the focus on physical white noise processes in order to validate our hypothesis.

Statistics of an Appealing Class of Random Processes

2021 ◽  
pp. 260-276
Author(s):  
Shaival Hemant Nagarsheth ◽  
Shambhu Nath Sharma
Keyword(s):  
White Noise ◽  
Stochastic Systems ◽  
Correction Term ◽  
Random Processes ◽  
Random Perturbations ◽  
White Noise Process ◽  
Coloured Noise ◽  
Diffusion Operator ◽  
Noise Process ◽  
Special Cases

The white noise process, the Ornstein-Uhlenbeck process, and coloured noise process are salient noise processes to model the effect of random perturbations. In this chapter, the statistical properties, the master's equations for the Brownian noise process, coloured noise process, and the OU process are summarized. The results associated with the white noise process would be derived as the special cases of the Brownian and the OU noise processes. This chapter also formalizes stochastic differential rules for the Brownian motion and the OU process-driven vector stochastic differential systems in detail. Moreover, the master equations, especially for the coloured noise-driven stochastic differential system as well as the OU noise process-driven, are recast in the operator form involving the drift and modified diffusion operators involving an additional correction term to the standard diffusion operator. The results summarized in this chapter will be useful for modelling a random walk in stochastic systems.

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