In this paper, we study a representation of generalized Mehler semigroup in terms of Fourier–Gauss transforms on white noise functionals and then we have an explicit form of the infinitesimal generator of the generalized Mehler semigroup in ter...
White noise generators can use uniform random sequences as a basis. However, such a technology may lead to deficient results if the original sequences have insufficient uniformity or omissions of random variables. This article offers a new approach f...
We characterize the dimension of Lie algebras of white noise operators containing the quantum white noise derivatives of the conservation operator. We establish isomorphisms to filiform Lie algebras, Engel-type algebras, and solvable Lie algebras wit...
Individuals with Autism Spectrum Disorder (ASD) often experience sensory hyperreactivities that interfere with daily life activities. White noise, characterized by its uniformity and its ability to mask environmental sounds, may serve as a tool to im...
In this paper, we propose a new notion, which we name S-contractive mapping, in a framework of vector-valued white noise functionals Wω⊗N⊂Γ(H)⊗K⊂(Wω⊗N)*. And we give concrete definitions of S-contractive...
The white-noise-driven KdV-type Boussinesq system is a class of stochastic partial differential equations (SPDEs) that describe nonlinear wave propagation under the influence of random noise—specifically white noise—and generalize feature...
This paper contributes significantly to time series analysis by discussing the empirical properties of white noise and their implications for model selection. This paper illustrates the ways in which the standard assumptions about white noise typical...
21 November 2022
Several models have tentatively associated improving attention-deficit/hyperactivity disorder (ADHD) symptoms with arousal and external environmental stimulation. In order to further clarify the relationships between ADHD symptoms, arousal, and exter...
The extended Kalman filter (EKF) has a wide range of applications (especially in power battery management systems) with a rapidly increasing market share. It aims to minimize the symmetric loss function (mean square error) and it has high accuracy an...
The qualitative theory for planar dynamical systems is used to study the bifurcation of the wave solutions for the space-fractional nonlinear Schrödinger equation with multiplicative white noise. Employing the first integral, we introduce some n...
Caused by nonlinear vibration, ocean white noise exhibits complex dynamic characteristics and nonlinear perception characteristics. To explore the potential application of ocean white noise in engineering and health fields, novel methods based on dee...
We investigate the stochastic dynamics of a prey-predator type ecosystem with time delay and the discrete random environmental fluctuations. In this model, the delay effect is represented by a time delay parameter and the effect of the environmental...
The goal of this paper is to design an effective Proportional Integral Derivative (PID) controller, which will control the active suspension system of a car, in order to eliminate the imposed vibration to the car from pavement. In this research, Gaus...
In this paper, we present an application of the renormalization group method developed by Chen, Goldenfeld and Oono for a stochastic differential equation in a space of Hilbert space-valued generalized random variables with multiplicative noise. The...
The current paper recovers dispersive optical solitons in birefringent fibers that are modeled by the Schrödinger–Hirota equation with differential group delay and white noise. Itô Calculus conducts the preliminary analysis. The G&pr...
Low-frequency noise investigation is a highly sensitive and very informative method for characterization of white nitride-based light-emitting diodes (LEDs) as well as for the evaluation of their degradation. We present a review of quality and reliab...
In extremely low-light conditions, random telegraph signal (RTS) noise and dark current white defects become visible. In this paper, a multi-aperture imaging system and selective averaging method which removes the RTS noise and the dark current white...
The microbiota in gastrointestinal tracts is recognized to play a pivotal role in the health of their hosts. Music and noise are prevalent environmental factors in human society and animal production and are reported to impact their welfare and physi...
To adaptively identify the modal parameters for time-invariant structures excited by non-white noise, this paper proposes a new operational modal analysis (OMA) method using hybrid neural networks. In this work, taking the acceleration response direc...
White Rabbit (WR) is an optical fibre-based time-frequency synchronization technology typically used in timekeeping laboratories for distributing time-frequency signals from a reference clock to distant locations. The accuracy of the received signals...
Since the prime days of stochastic hydrology back in 1960s, autoregressive (AR) and moving average (MA) models (as well as their extensions) have been widely used to simulate hydrometeorological processes. Initially, AR(1) or Markovian models with Ga...
14 June 2022
Existing research demonstrates that children with attention-deficit/hyperactivity disorder (ADHD) underperform in cognitive tasks involving working memory (WM) due to hypo-arousal, which has led to the development of arousal regulation models to dete...
The Constrained Disorder Principle (CDP) characterizes systems by their inherent variability, which is regulated within dynamic boundaries to ensure optimal function and adaptability. In biological systems, this variability, or “noise”, i...
Spatial discretization of the stochastic semi-linear subdiffusion equations driven by fractionally integrated multiplicative space-time white noise is considered. The nonlinear terms f and σ satisfy the global Lipschitz conditions and the linear grow...
The ultra-high frequency (UHF)-based partial discharge (PD) detection technology for gas-insulated switchgear (GIS) has achieved large-scale applications due to its high sensitivity and real-time monitoring capabilities. However, long-term service-in...
The additive Gaussian white noise (AGWN) level in real-life images is usually unknown, for which the empirical setting will make the denoising methods over-smooth fine structures or remove noise incompletely. The previous noise level estimation metho...
Without the assumption that the coefficient of weak damping is large enough, the existence of the global random attractors for simplified Von Karman plate without rotational inertia driven by either additive white noise or multiplicative white noise...
This work aims to address the P-bifurcation of a stochastic nonlinear system with fractional damping driven by Gaussian white noise. Based on a stochastic averaging method, a fractional damping stochastic nonlinear equation has been studied. Furtherm...
The thermodynamic Cucker–Smale model (TCS model) describes dynamic consistency caused by different temperatures between multi-agent particles. This paper studies the flocking behaviors of the TCS model with multiplicative white noise under hier...
Background/Objectives: This study evaluated the feasibility and effectiveness of three sound therapies—enriched acoustic environment with random noise (EAERR), enriched acoustic environment with gamma tones (EAEGT), and white noise (WN)—i...
A methane (CH4) sensor based on off-axis integrated cavity output spectroscopy (OA-ICOS) was developed, equipped with two measurement schemes: direct absorption spectroscopy (DAS) and wavelength modulation spectroscopy (WMS). The sensor used an optic...
In the present paper, the statistical responses of two-special prey–predator type ecosystem models excited by combined Gaussian and Poisson white noise are investigated by generalizing the stochastic averaging method. First, we unify the deterministi...
White noise is fundamentally linked to many processes; it has a flat power spectral density and a delta-correlated autocorrelation. Operators acting on white noise can result in coloured noise, whether they operate in the time domain, like fractional...
The modified exponentially weighted moving-average (modified EWMA) control chart is an improvement on the traditional EWMA control chart. Herein, we provide more details about the modified EWMA control chart using various values of an additional desi...
Stochastic partial differential equations have wide applications in various fields of science and engineering. This paper addresses the optical stochastic solitons and other exact stochastic solutions through birefringent fibers for the Biswas–...
This paper seeks to present the fundamental features of the category of conditional exponential convex functions (CECFs). Additionally, the study of continuous CECFs contributes to the characterization of convolution semigroups. In this context, we e...
This paper recovers dispersive gap solitons with the Kerr law of self-phase modulation and dispersive reflectivity. The enhanced direct algebraic method and the modified version of the sub-ODE approach have collectively made this retrieval possible....
In this paper, we investigate the Cauchy problem for the coupled generalized Korteweg–de Vries system driven by a cylindrical Wiener process. We prove local well-posedness for data in Hs×Hs, with s>12. The key methods that we used in t...
Partial discharge (PD) detection plays an important role in online condition monitoring of electrical equipment and power cables. However, the noise of PD measurement will significantly reduce the performance of the detection algorithm. In this paper...
Stochastic Differential Equations (SDEs) model physical phenomena dominated by stochastic processes. They represent a method for studying the dynamic evolution of a physical phenomenon, like ordinary or partial differential equations, but with an add...
The main purpose of this paper is to study the dynamics and embedded solitons of stochastic quadratic and cubic nonlinear susceptibilities in the Itô sense, which can further help researchers understand the propagation of soliton nonlinear syst...
We study the (3+1)-dimensional stochastic Jimbo–Miwa (SJM) equation induced by multiplicative white noise in the Itô sense. We employ the Riccati equation mapping and He’s semi-inverse techniques to provide trigonometric, hyperbolic...
In this article, the stochastic Riemann wave equation (SRWE) forced by white noise in the Itô sense is considered. The extended tanh function and mapping methods are applied to obtain new elliptic, rational, hyperbolic, and trigonometric stochastic s...
In the current study, we investigate the stochastic Benjamin–Bona–Mahony equation with beta derivative (SBBME-BD). The considered stochastic term is the multiplicative noise in the Itô sense. By combining the F-expansion approach wi...
We investigate the spatial discretization of a stochastic semilinear superdiffusion problem driven by fractionally integrated multiplicative space–time white noise. The white noise is characterized by its properties of being white in both space...
Online partial discharge (PD) detection for power cables is one reliable means of monitoring their health. However, strong interference by white noise poses a major challenge in the process of collecting information on partial discharge signals. To s...
In singular spectrum analysis, which is applied to signal extraction, it is of critical importance to select the number of components correctly in order to accurately estimate the signal. In the case of a low-rank signal, there is a challenge in esti...
For the first time, we study the Fokas–Lenells equation in polarization preserving fibers with multiplicative white noise in Itô sense. Four integration algorithms are applied, namely, the method of modified simple equation (MMSE), the me...
As the noise power increases, the target signal features become less obvious, which leads to the failure of weak signal detection methods. To address this problem, a quantum weak signal detection method, Local Semi-Classical Signal Analysis-Singular...
In this study, the maximum error-free transmission rate of an additive white Gaussian noise channel with a symmetric analog-to-digital converter (ADC) was derived as a composite function of the binary entropy function, Gaussian Q-function, and the sq...
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