A GENERAL FORM OF THE INCREMENTS OF A TWO-PARAMETER WIENER PROCESS

In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.

Optimization study of station track utilization in high-speed railroad based on constraints of control in random origin and process

Purpose-The purpose of this paper is to eliminate the fluctuations in train arrival and departure times caused by skewed distributions in interval operation times.These fluctuations arise from random origin and process factors during interval operations and can accumulate over multiple intervals.The aim is to enhance the robustness of high-speed rail station arrival and departure track utilization schemes.Design/methodologylapproach-To achieve this objective,the paper simulates actual train operations,incorporating the fluctuations in interval operation times into the utilization of arrival and departure tracks at the station.The Monte Carlo simulation method is adopted to solve this problem.This approach transforms a nonlinear model,which includes constraints from probability distribution functions and is difficult to solve directly,into a linear programming model that is easier to handle.The method then linearly weights two objectives to optimize the solution.Findings-Through the application of Monte Carlo simulation,the study successfully converts the complex nonlinear model with probability distribution function constraints into a manageable linear programming model.By continuously adjusting the weighting coefficients of the linear objectives,the method is able to optimize the Pareto solution.Notably,this approach does not require extensive scene data to obtain a satisfactory Pareto solution set.Originality/value-The paper contributes to the field by introducing a novel method for optimizing high-speed rail station arrival and departure track utilization in the presence of fluctuations in interval operation times.The use of Monte Carlo simulation to transform the problem into a tractable linear programming model represents a significant advancement.Furthermore,the method's ability to produce satisfactory Pareto solutions without relying on extensive data sets adds to its practical value and applicability in real-world scenarios.

A HybridManufacturing ProcessMonitoringMethod Using Stacked Gated Recurrent Unit and Random Forest

This study proposed a new real-time manufacturing process monitoring method to monitor and detect process shifts in manufacturing operations.Since real-time production process monitoring is critical in today’s smart manufacturing.The more robust the monitoring model,the more reliable a process is to be under control.In the past,many researchers have developed real-time monitoring methods to detect process shifts early.However,thesemethods have limitations in detecting process shifts as quickly as possible and handling various data volumes and varieties.In this paper,a robust monitoring model combining Gated Recurrent Unit(GRU)and Random Forest(RF)with Real-Time Contrast(RTC)called GRU-RF-RTC was proposed to detect process shifts rapidly.The effectiveness of the proposed GRU-RF-RTC model is first evaluated using multivariate normal and nonnormal distribution datasets.Then,to prove the applicability of the proposed model in a realmanufacturing setting,the model was evaluated using real-world normal and non-normal problems.The results demonstrate that the proposed GRU-RF-RTC outperforms other methods in detecting process shifts quickly with the lowest average out-of-control run length(ARL1)in all synthesis and real-world problems under normal and non-normal cases.The experiment results on real-world problems highlight the significance of the proposed GRU-RF-RTC model in modern manufacturing process monitoring applications.The result reveals that the proposed method improves the shift detection capability by 42.14%in normal and 43.64%in gamma distribution problems.

Remaining useful life estimation based on Wiener degradation processes with random failure threshold

Remaining useful life(RUL) estimation based on condition monitoring data is central to condition based maintenance(CBM). In the current methods about the Wiener process based RUL estimation, the randomness of the failure threshold has not been studied thoroughly. In this work, by using the truncated normal distribution to model random failure threshold(RFT), an analytical and closed-form RUL distribution based on the current observed data was derived considering the posterior distribution of the drift parameter. Then, the Bayesian method was used to update the prior estimation of failure threshold. To solve the uncertainty of the censored in situ data of failure threshold, the expectation maximization(EM) algorithm is used to calculate the posteriori estimation of failure threshold. Numerical examples show that considering the randomness of the failure threshold and updating the prior information of RFT could improve the accuracy of real time RUL estimation.

ON DESIGN METHOD OF THE PRECISION CAM PROFILE WITH RANDOM PROCESSING ERRORS

Based on probability and statistic, a design method of precision cam profileconcerning the influence of random processing errors is advanced. Combining the design with theprocess, which can be used to predict that cam profiles will be successfully processed or not in thedesign stage, design of the cam can be done by balancing the economization and reliability. Inaddition, an fuzzy deduction method based on Bayers formula is advanced to estimate processingreasonable of the designed precision cam profile, and it take few samples.

THE CONSTRUCTION OF DENUMERABLE q-PROCESSES IN RANDOM ENVIRONMENTS-THE EXISTENCE AND UNIQUENESS

The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.

A Novel 2-D Signal Processing Scheme for Quasi-Random Step Frequency Signal

Due to the heavy congestion in HF bands, HF radars are restricted to operating within narrow frequency bands. To improve the system bandwidth and avoid heavy interference bands, a quasi-random step frequency signal with discontinuous bands is presented. A novel two-dimensional signal processing scheme for this signal is proposed on the basis of delicate signal analysis. Simulation results demonstrate that the scheme could successfully realize the resolutions by decoupling the range-Doppler ambiguity, and effectively suppress the maximal sidelobe. Moreover, the scheme is simple and has good numerical stability.

THE CONSTRUCTION OF DENUMERABLE q-PROCESSES IN RANDOM ENVIRONMENTS SATISFYING (F) OR (B)

This article is a continuation of[9].Based on the discussion of random Kolmogorov forward（backward）equations,for any given q-matrix in random environment, Q（θ）=（q（θ;x,y）,x,y∈X）,an infinite class of q-processes in random environments satisfying the random Kolmogorov forward（backward）equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward（backward）equation are constructed.

THE ERGODICITY FOR BI-IMMIGRATION BIRTH AND DEATH PROCESSES IN RANDOM ENVIRONMENT

The concepts of bi-immigration birth and death density matrix in random environment and bi-immigration birth and death process in random environment are introduced. For any bi-immigration birth and death matrix in random environment Q（θ） with birth rate λ 〈 death rate μ, the following results are proved, （1） there is an unique q-process in random environment, P^-（θ＊（0）;t） = （p^-（θ^＊（0）;t,i,j）,i,j ≥ 0）, which is ergodic, that is, lim t→∞（θ^＊（0）;t,i,j） = π^-（θ^＊（0）;j） ≥0 does not depend on i ≥ 0 and ∑j≥0π （θ＊（0）;j） = 1, （2） there is a bi-immigration birth and death process in random enjvironment （X^＊ = {X^＊,t ≥ 0},ε^＊ = {εt,t ∈ （-∞, ∞）}） with random transition matrix P^-（θ^＊ （0）;t） such that X^＊ is a strictly stationary process.

MOMENTS OF CONTINUOUS-STATE BRANCHING PROCESSES IN LéVY RANDOM ENVIRONMENTS

For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuous function satisfying some standard conditions.

LIMIT THEOREMS FOR A GALTON-WATSON PROCESS IN THE I.I.D. RANDOM ENVIRONMENT

In this article, we obtain the central limit theorem and the law of the iterated logarithm for Galton-Watson processes in i.i.d, random environments.

MOMENTS AND LARGE DEVIATIONS FOR SUPERCRITICAL BRANCHING PROCESSES WITH IMMIGRATION IN RANDOM ENVIRONMENTS

Let(Z_(n))be a branching process with immigration in a random environmentξ,whereξis an independent and identically distributed sequence of random variables.We show asymptotic properties for all the moments of Z_(n) and describe the decay rates of the n-step transition probabilities.As applications,a large deviation principle for the sequence log Z_(n) is established,and related large deviations are also studied.

A note on asymptotic behavior of Galton-Watson branching processes in random environments

In this paper, we investigate Galton-Watson branching processes in random environments. In the case where the environmental process is a Markov chain which is positive recurrent or has a transition matrix Q (θ,α) such that sup_θ Q (θ,α)> 0 for some α, we prove that the model has the asymptotic behavior being similar to that of Galton-Watson branching processes. In other case where the environments are non-stationary independent, the sufficient conditions are obtained for certain extinction and uncertain extinction for the model.

FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES

This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hausdorff dimension and capacity.

CENTRAL LIMIT THEOREM AND CONVERGENCE RATES FOR A SUPERCRITICAL BRANCHING PROCESS WITH IMMIGRATION IN A RANDOM ENVIRONMENT

We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.

Laplace Transformation and Ergodic Potential Kernel for q-Process in Random Environment

This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.

Application of Random Process in Soil Profile Modeling

When using the random process in soil profile modeling, the stationary and ergodicity of the soil properties in the profile must be tested. This paper describes a procedure for stationary and ergodicity testing. Numerical examples were given for demonstration. A log-cosine function is suggested to simulate the correlation function, which has been proved to be good for soil profile modeling.

Limit theorems for supremum of Gaussian processes over a random interval

Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.

Simulation study on characteristics of long-range interaction in randomly asymmetric exclusion process

In this paper we investigate the dynamics of an asymmetric exclusion process on a one-dimensional lattice with long- range hopping and random update via Monte Carlo simulations theoretically. Particles in the model will firstly try to hop over successive unoccupied sites with a probability q, which is different from previous exclusion process models. The probability q may represent the random access of particles. Numerical simulations for stationary particle currents, density profiles, and phase diagrams are obtained. There are three possible stationary phases： the low density （LD） phase, high density （HD） phase, and maximal current （MC） in the system, respectively. Interestingly, bulk density in the LD phase tends to zero, while the MC phase is governed by α,β, and q. The HD phase is nearly the same as the normal TASEP, determined by exit rate β. Theoretical analysis is in good agreement with simulation results. The proposed model may provide a better understanding of random interaction dynamics in complex systems.

Definition of Laplace Transforms for Distribution of the First Passage of Zero Level of the Semi-Markov Random Process with Positive Tendency and Negative Jump

One of the important problems of stochastic process theory is to define the Laplace transforms for the distribution of semi-markov random processes. With this purpose, we will investigate the semimarkov random processes with positive tendency and negative jump in this article. The first passage of the zero level of the process will be included as a random variable. The Laplace transforms for the distribution of this random variable is defined. The parameters of the distribution will be calculated on the basis of the final results.