212 Results Found

This article is devoted to methods of processing random processes. This task becomes particularly relevant in cases where the random process is broadband and non-stationary; then, the measurement of a random process can be associated with an assessme...

We develop a design-conditional limit theory for kernel estimators of conditional U-functionals based on locally stationary functional random fields observed at irregular random locations and under incomplete response observation. The covariates take...

This paper develops asymptotic theory for kernel estimation of density-weighted conditional functionals and regression derivatives when responses are missing at random (MAR) and the observations form a strictly stationary ergodic process. Sequential...

Stute presented the so-called conditional U-statistics generalizing the Nadaraya–Watson estimates of the regression function. Stute demonstrated their pointwise consistency and the asymptotic normality. In this paper, we extend the results to a...

In his work published in (Ann. Probab. 19, No. 2 (1991), 812–825), W. Stute introduced the notion of conditional U-statistics, expanding upon the Nadaraya–Watson estimates used for regression functions. Stute illustrated the pointwise con...

The high-dimensional stochastic space caused by a large number of random variables remains a significant challenge hindering the practical application of stochastic process simulation in engineering. Although various dimension reduction techniques ha...

It is shown that the inert properties of a stationary random process can be expressed in terms of the ratio of its correlation interval ${\tau }_x$ to the doubled variance D_x. When using a fixed value of Planck’s constant h as a proportionality fact...

Random vibration analysis is a mathematical tool that offers great advantages in predicting the mechanical response of structural systems subjected to external dynamic loads whose nature is intrinsically stochastic, as in cases of sea waves, wind pre...

The Lambert W is a Bernstein function and hence the cumulant function of a positive infinitely divisible law, the Lambert law $L(\Lambda )$. The Lambert law is self-decomposable with a unit rate compound Poisson background driving Lévy process (...

In engineering, the study of the dynamic response of structures subjected to non-deterministically variable loads is particularly important, especially when considering the damage that such loads can cause due to fatigue phenomena. This is the case,...

In working processes, mechanical systems are often affected by both internal and external forces, which are the cause of the forced vibrations of the structures. They can be destroyed if the amplitude of vibration reaches a high enough value. One of...

In this paper, we obtain the law of iterated logarithm for linear processes in sub-linear expectation space. It is established for strictly stationary independent random variable sequences with finite second-order moments in the sense of non-additive...

The first hitting time of a boundary or threshold by the sample path of a stochastic process is the central concept of threshold regression models for survival data analysis. Regression functions for the process and threshold parameters in these mode...

In the current fatigue life calculation theory, the most commonly used method is the frequency domain method. However, most of the frequency domain fatigue life prediction models do not indicate the scope of the application of the spectral width para...

We consider the estimation of partial derivatives of multivariate regression-type functionals from incomplete observations generated by a discrete-time strictly stationary ergodic process. The response variable is subject to a missing-at-random (MAR)...

Motivated by a simple model of earthquake statistics, a finite random discrete dynamical system is defined in order to obtain Catalan number recurrence by describing the stationary state of the system in the limit of its infinite size. Equations desc...

We study the small-radius topology of the Euclidean tube generated by a smooth planar Gaussian path. Let $X={\left(X_t\right)}_{0\le t\le T}$ be a sufficiently regular Gaussian process with values in ${\mathbb{R}}^2$, and define its radius-$\epsilon$ tube by ${\mathcal{T}}_{\epsilon }=\{x\in {\mathbb{R}}^2:dis$...

A method for obtaining integer sequences is presented by defining simple rules for the evolution of a discrete dynamical system. This paper demonstrates that various Catalan-like recurrences of known integer sequences can be obtained from a single st...

Ship acoustic signal classification is essential for vessel identification, underwater navigation, and maritime security. Traditional methods struggle with the non-stationary nature and noise of ship acoustic signals, reducing classification accuracy...

This paper develops a pointwise distributional theory for linear wavelet density and regression estimation from randomly right-censored observations exhibiting stationary ergodic dependence. In contrast to the prevailing literature, which typically r...

We propose the entropy of random Markov trajectories originating and terminating at the same state as a measure of the stability of a state of a Markov process. These entropies can be computed in terms of the entropy rates and stationary distribution...

The soil parameters of artificial soil foundations exhibit significant spatial variability due to particle sorting during the filling process, which follows a trend that is distinct from that of natural soft foundations. Based on this observation, a...

The article deals with queueing systems with random resource requirements modeled as bivariate Markov jump processes. One of the process components describes the service system with limited resources. Another component represents a random environment...

The theoretical and experimental evaluation of the cyclostationary random data transferring process corrupted by the individually and jointly cyclostationary crosstalk interference is presented. The interference and the message signals were measured...

In this paper, we consider a randomized TB model with two treatment modalities, home treatment and hospital treatment, in which ${\beta }_1$ and ${\beta }_2$ satisfy the log-normal Ornstein–Uhlenbeck process. First, we prove the local stability of the po...

Recently, as one of the intelligent transportation systems, radar systems that monitor traffic on the road have received attention. To ensure the reliable detection performance of the traffic monitoring radar, it is necessary to distinguish stationar...

Since correlated stochastic processes are often presented in practical problems, feasible methods to model and generate correlated processes appropriately are needed for analysis and simulation. The present paper systematically presents three methods...

This paper searches for stochastic trends and returns predictability in key energy asset markets in Europe over the last decade. The financial assets include Intercontinental Exchange Futures Europe (ICE-ECX) carbon emission allowances (the main driv...

Timely diagnosis and prognosis based on degradation symptoms are essential steps for condition-based maintenance (CBM) to guarantee industrial safety and productivity. Most industrial machines operate under variable operating conditions. This time-va...

Integrating the general expression of the generalized harmonic wavelet (GHW)-based spectral representation method (SRM) and the idea of stochastic harmonic function (SHF), a novel stochastic generalized harmonic wavelet (SGHW) method for fully nonsta...

From the viewpoint of statistical physics, ecosystems in the real world are very attractive targets of research as examples of far-from thermal equilibrium systems where various kinds of components are coming in and out continuously while keeping the...

In this work, the case of a Cox Process with Folded Normal Intensity (CP-FNI), in which the intensity is given by $\mathrm{\Lambda }\left(t\right)=\left|Z\right(t\left)\right|$, where $Z\left(t\right)$ is a stationary Gaussian process, is studied. Here, two particular cases are dealt with: (i) when the pro...

Machinery with several rotating and stationary components tends to produce non-stationary and random vibration signatures due to the fluctuations in the input loads and process defects due to long hours of operation. Traditional heuristics methods ar...

The current paper is devoted to the dynamical property of the stochastic Cox–Ingersoll–Ross (CIR) model with pure jump noise, which is an extension of the CIR model. Firstly, we characterize the existence and 2-moment of the CIR process w...

We study the thermodynamic limit of very long walks on finite, connected, non-random graphs subject to possible random modifications and transportation capacity noise. As walks might represent the chains of interactions between system units, statisti...

In this paper, we provide a central limit theorem for the finite-dimensional marginal distributions of empirical processes ${\left(Z_n\left(f\right)\right)}_{f\in \mathcal{F}}$ whose index set $\mathcal{F}$ is a family of cluster functionals valued on blocks of values of a stationary random field. T...

The dynamics of a stochastic system that exhibits large fluctuations to a given state are almost deterministic due to weak random perturbations. Such large fluctuations occur with overwhelming probability in the vicinity of the so-called optimal path...

The spatial formation of coherent random laser modes in strongly scattering disordered random media is a central feature in the understanding of the physics of random lasers. We derive a quantum field theoretical method for random lasing in disordere...

We analyze two-dimensional isotropic heterogeneous diffusion with a radially decaying diffusion coefficient $D\left(\rho \right)=D_0/{\rho }^2$, subject to Poissonian stochastic resetting to the origin. Since multiplicative noise makes the process interpretation-depe...

As we discuss, a stationary stochastic process is nonergodic when a random persistent topic can be detected in the infinite random text sampled from the process, whereas we call the process strongly nonergodic when an infinite sequence of independent...

Two-sample and independence tests with the kernel-based mmd and hsic have shown remarkable results on i.i.d. data and stationary random processes. However, these statistics are not directly applicable to nonstationary random processes, a prevalent fo...

This study outlines the development and optimization of a Long Short-Term Memory (LSTM) network designed to analyze and classify time-series data from tribological experiments, with a particular emphasis on identifying stationary phases. The process...

This article presents an overview of methodologies for spatial prediction of functional data, focusing on both stationary and non-stationary conditions. A significant aspect of the functional random fields analysis is evaluating stationarity to chara...

The one dimensional discrete scan statistic is considered over sequences of random variables generated by block factor dependence models. Viewed as a maximum of an 1-dependent stationary sequence, the scan statistics distribution is approximated with...

An $MAP/PH/N$-type queuing system functioning within a finite-state Markovian random environment is studied. The random environment’s state impacts the number of available servers, the underlying processes of customer arrivals and service, and th...

We revise and slightly generalize some variational problems related to the “informational approach” in the classical optimization problem for automatic control systems which was popular from 1970–1990. We find extremals for various...

This paper considers a tandem queueing network with a Poisson arrival process of incoming calls, two servers, and two infinite orbits by the method of asymptotic analysis. The servers provide services for incoming calls for exponentially distributed...

This work introduces a hybrid memory-based random walk model that combines the Elephant Random Walk with a modified Moran Random Walk. The model introduces a sequence of independent and identically distributed random variables with mean 1, representi...

The article considers stationary and dynamic distributions of news by the number of comments. The processing of the observed data showed that static distribution of news by the number of comments relating to that news obeys a power law, and the dynam...

We consider a sequence of i.i.d. random variables, $\left(\mathbf{\xi }\right)={\left({\xi }_i\right)}_{i=0,1,2,\cdots }$, $\mathbb{E}{\xi }_0=0$, $\mathbb{E}{\xi }_0^2=1$, and subordinate it by a doubly stochastic Poisson process $\mathsf{\Pi }\left(\lambda t\right)$, where $\lambda \ge 0$ is a random variable and $\mathsf{\Pi }$ is a standard Poisson...