Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers s...Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers satisfying ∑j=0^∞｜aj｜〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E｜ε1｜^2＋δ′〈 for some δ′〉0 and μ（n）=O（n^-ρ） for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}.展开更多
This paper considers the estimation problem of a variance change-point in linear process.Consistency of a SCUSUM type change-point estimator is proved and its rate of convergence is established.The mean-unknown case i...This paper considers the estimation problem of a variance change-point in linear process.Consistency of a SCUSUM type change-point estimator is proved and its rate of convergence is established.The mean-unknown case is also considered.展开更多
In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expec...In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expectations initiated by Peng[19].It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's central limit theorem and invariance principle to the case where probability measures are no longer additive.展开更多
In this paper,we introduce a new concept,namelyε-arithmetics,for real vectors of any fixed dimension.The basic idea is to use vectors of rational values(called rational vectors)to approximate vectors of real values o...In this paper,we introduce a new concept,namelyε-arithmetics,for real vectors of any fixed dimension.The basic idea is to use vectors of rational values(called rational vectors)to approximate vectors of real values of the same dimension withinεrange.For rational vectors of a fixed dimension m,they can form a field that is an mth order extension Q(α)of the rational field Q whereαhas its minimal polynomial of degree m over Q.Then,the arithmetics,such as addition,subtraction,multiplication,and division,of real vectors can be defined by using that of their approximated rational vectors withinεrange.We also define complex conjugate of a real vector and then inner product and convolutions of two real vectors and two real vector sequences(signals)of finite length.With these newly defined concepts for real vectors,linear processing,such as linear filtering,ARMA modeling,and least squares fitting,can be implemented to real vectorvalued signals with real vector-valued coefficients,which will broaden the existing linear processing to scalar-valued signals.展开更多
In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form Xt =∑j^∞=∞ Aj∈t-j,where {∈n, n ∈ Z} is a sequence of END stochastically dominated ran...In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form Xt =∑j^∞=∞ Aj∈t-j,where {∈n, n ∈ Z} is a sequence of END stochastically dominated random variables and {An,n ∈ Z} is a sequence of random varibles. As applications, the convergence rate, Marcinkiewicz-Zvgmund strong law and strong law of large numbers for this linear process are established.展开更多
An air classifier is used in the recycling process of covered electric wire in the recycling factories, in which the covered electric wires are crushed, sieved, and classified by the air classifier, which generates wa...An air classifier is used in the recycling process of covered electric wire in the recycling factories, in which the covered electric wires are crushed, sieved, and classified by the air classifier, which generates wastes. In these factories, operators manually adjust the air flow rate while checking the wastes discharged from the separator outlet. However, the adjustments are basically done by trial and error, and it is difficult to do them appropriately. In this study, we tried to develop the image processing system that calculates the ratio of copper (Cu) product and polyvinyl chloride (PVC) in the wastes as a substitute for the operator’s eyes. Six colors of PVC (white, gray, green, blue, black, and red) were used in the present work. An image consists of foreground and background. An image’s regions of interest are objects (Cu particles) in its foreground. However, the particles having a color similar to the background color are buried in the background. Using the difference of two color backgrounds, we separated particles and background without dependent of background. The Otsu’ thresholding was employed to choose the threshold to maximize the degree of separation of the particles and background. The ratio of Cu to PVC pixels from mixed image was calculated by linear discriminant analysis. The error of PVC pixels resulted in zero, whereas the error of Cu pixels arose to 4.19%. Comparing the numbers of Cu and PVC pixels within the contour, the minority of the object were corrected to the majority of the object. The error of Cu pixels discriminated as PVC incorrectly became zero percent through this correction.展开更多
The Linear Gaussian white noise process is an independent and identically distributed (iid) sequence with zero mean and finite variance with distribution N (0, σ2 ) . Hence, if X1, x2, …, Xn is a realization of such...The Linear Gaussian white noise process is an independent and identically distributed (iid) sequence with zero mean and finite variance with distribution N (0, σ2 ) . Hence, if X1, x2, …, Xn is a realization of such an iid sequence, this paper studies in detail the covariance structure of X1d, X2d, …, Xnd, d=1, 2, …. By this study, it is shown that: 1) all powers of a Linear Gaussian White Noise Process are iid but, not normally distributed and 2) the higher moments (variance and kurtosis) of Xtd, d=2, 3, … can be used to distinguish between the Linear Gaussian white noise process and other processes with similar covariance structure.展开更多
A method of data processing to determine the coefficients of linearization equations for 1050 anemometer (produced by Thermo-Systems Inc. -TSI, USA) with the sensors made of domestic hot wire using the program preferr...A method of data processing to determine the coefficients of linearization equations for 1050 anemometer (produced by Thermo-Systems Inc. -TSI, USA) with the sensors made of domestic hot wire using the program preferred in this Paper is described. By calculation and test, it is indicated that the error resulting from this method is about 0. 5% of the full scale and less than TSl's. By using this method we can set up the calibration curve according to the measurement range and the diameter of the hot wire at a certain accuracy.展开更多
In this work, we used a linear CCD to detect the whole physical developing process of silver diffusion transfer reversal process in photographic chemistry. The influence of the ingredient of the working solution was s...In this work, we used a linear CCD to detect the whole physical developing process of silver diffusion transfer reversal process in photographic chemistry. The influence of the ingredient of the working solution was studied.展开更多
Accurate classification and prediction of future traffic conditions are essential for developing effective strategies for congestion mitigation on the highway systems. Speed distribution is one of the traffic stream p...Accurate classification and prediction of future traffic conditions are essential for developing effective strategies for congestion mitigation on the highway systems. Speed distribution is one of the traffic stream parameters, which has been used to quantify the traffic conditions. Previous studies have shown that multi-modal probability distribution of speeds gives excellent results when simultaneously evaluating congested and free-flow traffic conditions. However, most of these previous analytical studies do not incorporate the influencing factors in characterizing these conditions. This study evaluates the impact of traffic occupancy on the multi-state speed distribution using the Bayesian Dirichlet Process Mixtures of Generalized Linear Models (DPM-GLM). Further, the study estimates the speed cut-point values of traffic states, which separate them into homogeneous groups using Bayesian change-point detection (BCD) technique. The study used 2015 archived one-year traffic data collected on Florida’s Interstate 295 freeway corridor. Information criteria results revealed three traffic states, which were identified as free-flow, transitional flow condition (congestion onset/offset), and the congested condition. The findings of the DPM-GLM indicated that in all estimated states, the traffic speed decreases when traffic occupancy increases. Comparison of the influence of traffic occupancy between traffic states showed that traffic occupancy has more impact on the free-flow and the congested state than on the transitional flow condition. With respect to estimating the threshold speed value, the results of the BCD model revealed promising findings in characterizing levels of traffic congestion.展开更多
It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those w...It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those who have finite number of descendants. In this paper we analyze such a decomposition for the linear-fractional Bienayme-Galton-Watson processes with countably many types. We find explicit expressions for the main characteristics of the reproduction laws for so-called skeleton and doomed particles.展开更多
In this paper,a dynamic linear detecting method,that the non-linear coefficient NL% was led and the non-linearity of data were estimated continuously and dynamically and determined when NL% exceeded reference value (...In this paper,a dynamic linear detecting method,that the non-linear coefficient NL% was led and the non-linearity of data were estimated continuously and dynamically and determined when NL% exceeded reference value (5%),was used for data processing and could solve the problem caused by the phenomenon of substrate depleting occurred following the redox reaction in portable blood sugar analyzer.By contrast to the conventional end-point method,the dynamic linear detecting method is based on multipoint data collecting.Experiments of measuring the calibration glucose solution with 8 various concentrations from 50 mg/dl to 400 mg/dl were carried out with the analyzer developed by our group.The linear regression curve,whose correlation for the data was 0.9995 and the residual was 2.8080,were obtained.The obtained correlation,residual, and the computation workload are all fit for the portable blood sugar analyzer.展开更多
Let {Xt,t ≥ 1} be a moving average process defined by Xt = ∑^∞ k=0 αkξt-k, where {αk,k ≥ 0} is a sequence of real numbers and {ξt,-∞ 〈 t 〈 ∞} is a doubly infinite sequence of strictly stationary dependen...Let {Xt,t ≥ 1} be a moving average process defined by Xt = ∑^∞ k=0 αkξt-k, where {αk,k ≥ 0} is a sequence of real numbers and {ξt,-∞ 〈 t 〈 ∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {αk, k ≥ 0} which entail that {Xt, t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt, t ≥ 1} to a Gaussian process is studied. Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.展开更多
基金National Natural Science Foundation of China(10571073).
文摘Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers satisfying ∑j=0^∞｜aj｜〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E｜ε1｜^2＋δ′〈 for some δ′〉0 and μ（n）=O（n^-ρ） for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}.
基金Supported by Foundation of Education Department of Shaanxi Provincial Government（2010JK561） Supported by Basic Research Foundation of Xi’an Polytechnic University（2010JC07）+1 种基金 Supported by the Special Funds of the National Natural Science Foundation of China（11026135） Supported by Chinese Ministry of Education Funds for Young Scientists（10YJC910007）
文摘This paper considers the estimation problem of a variance change-point in linear process.Consistency of a SCUSUM type change-point estimator is proved and its rate of convergence is established.The mean-unknown case is also considered.
基金Supported by the National Natural Science Foundation of China(11771178)the Science and Technology Development Program of Jilin Province(20170101152JC)+1 种基金the Science and Technology Program of Jilin Edu-cational Department during the“13th Five-Year”Plan Period(JJKH20200951KJ)Fundamental Research Funds for the Central Universities。
文摘In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expectations initiated by Peng[19].It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's central limit theorem and invariance principle to the case where probability measures are no longer additive.
文摘In this paper,we introduce a new concept,namelyε-arithmetics,for real vectors of any fixed dimension.The basic idea is to use vectors of rational values(called rational vectors)to approximate vectors of real values of the same dimension withinεrange.For rational vectors of a fixed dimension m,they can form a field that is an mth order extension Q(α)of the rational field Q whereαhas its minimal polynomial of degree m over Q.Then,the arithmetics,such as addition,subtraction,multiplication,and division,of real vectors can be defined by using that of their approximated rational vectors withinεrange.We also define complex conjugate of a real vector and then inner product and convolutions of two real vectors and two real vector sequences(signals)of finite length.With these newly defined concepts for real vectors,linear processing,such as linear filtering,ARMA modeling,and least squares fitting,can be implemented to real vectorvalued signals with real vector-valued coefficients,which will broaden the existing linear processing to scalar-valued signals.
基金Supported by the National Natural Science Foundation of China (No.10071072)the project supported by Natural Science Fundation of Zhejiang Province (No.101016).
文摘In this paper, we obtain the invariance principle for linear processes generated by a negatively associated sequence.
文摘In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form Xt =∑j^∞=∞ Aj∈t-j,where {∈n, n ∈ Z} is a sequence of END stochastically dominated random variables and {An,n ∈ Z} is a sequence of random varibles. As applications, the convergence rate, Marcinkiewicz-Zvgmund strong law and strong law of large numbers for this linear process are established.
文摘An air classifier is used in the recycling process of covered electric wire in the recycling factories, in which the covered electric wires are crushed, sieved, and classified by the air classifier, which generates wastes. In these factories, operators manually adjust the air flow rate while checking the wastes discharged from the separator outlet. However, the adjustments are basically done by trial and error, and it is difficult to do them appropriately. In this study, we tried to develop the image processing system that calculates the ratio of copper (Cu) product and polyvinyl chloride (PVC) in the wastes as a substitute for the operator’s eyes. Six colors of PVC (white, gray, green, blue, black, and red) were used in the present work. An image consists of foreground and background. An image’s regions of interest are objects (Cu particles) in its foreground. However, the particles having a color similar to the background color are buried in the background. Using the difference of two color backgrounds, we separated particles and background without dependent of background. The Otsu’ thresholding was employed to choose the threshold to maximize the degree of separation of the particles and background. The ratio of Cu to PVC pixels from mixed image was calculated by linear discriminant analysis. The error of PVC pixels resulted in zero, whereas the error of Cu pixels arose to 4.19%. Comparing the numbers of Cu and PVC pixels within the contour, the minority of the object were corrected to the majority of the object. The error of Cu pixels discriminated as PVC incorrectly became zero percent through this correction.
文摘The Linear Gaussian white noise process is an independent and identically distributed (iid) sequence with zero mean and finite variance with distribution N (0, σ2 ) . Hence, if X1, x2, …, Xn is a realization of such an iid sequence, this paper studies in detail the covariance structure of X1d, X2d, …, Xnd, d=1, 2, …. By this study, it is shown that: 1) all powers of a Linear Gaussian White Noise Process are iid but, not normally distributed and 2) the higher moments (variance and kurtosis) of Xtd, d=2, 3, … can be used to distinguish between the Linear Gaussian white noise process and other processes with similar covariance structure.
文摘A method of data processing to determine the coefficients of linearization equations for 1050 anemometer (produced by Thermo-Systems Inc. -TSI, USA) with the sensors made of domestic hot wire using the program preferred in this Paper is described. By calculation and test, it is indicated that the error resulting from this method is about 0. 5% of the full scale and less than TSl's. By using this method we can set up the calibration curve according to the measurement range and the diameter of the hot wire at a certain accuracy.
文摘In this work, we used a linear CCD to detect the whole physical developing process of silver diffusion transfer reversal process in photographic chemistry. The influence of the ingredient of the working solution was studied.
文摘Accurate classification and prediction of future traffic conditions are essential for developing effective strategies for congestion mitigation on the highway systems. Speed distribution is one of the traffic stream parameters, which has been used to quantify the traffic conditions. Previous studies have shown that multi-modal probability distribution of speeds gives excellent results when simultaneously evaluating congested and free-flow traffic conditions. However, most of these previous analytical studies do not incorporate the influencing factors in characterizing these conditions. This study evaluates the impact of traffic occupancy on the multi-state speed distribution using the Bayesian Dirichlet Process Mixtures of Generalized Linear Models (DPM-GLM). Further, the study estimates the speed cut-point values of traffic states, which separate them into homogeneous groups using Bayesian change-point detection (BCD) technique. The study used 2015 archived one-year traffic data collected on Florida’s Interstate 295 freeway corridor. Information criteria results revealed three traffic states, which were identified as free-flow, transitional flow condition (congestion onset/offset), and the congested condition. The findings of the DPM-GLM indicated that in all estimated states, the traffic speed decreases when traffic occupancy increases. Comparison of the influence of traffic occupancy between traffic states showed that traffic occupancy has more impact on the free-flow and the congested state than on the transitional flow condition. With respect to estimating the threshold speed value, the results of the BCD model revealed promising findings in characterizing levels of traffic congestion.
文摘It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those who have finite number of descendants. In this paper we analyze such a decomposition for the linear-fractional Bienayme-Galton-Watson processes with countably many types. We find explicit expressions for the main characteristics of the reproduction laws for so-called skeleton and doomed particles.
文摘In this paper,a dynamic linear detecting method,that the non-linear coefficient NL% was led and the non-linearity of data were estimated continuously and dynamically and determined when NL% exceeded reference value (5%),was used for data processing and could solve the problem caused by the phenomenon of substrate depleting occurred following the redox reaction in portable blood sugar analyzer.By contrast to the conventional end-point method,the dynamic linear detecting method is based on multipoint data collecting.Experiments of measuring the calibration glucose solution with 8 various concentrations from 50 mg/dl to 400 mg/dl were carried out with the analyzer developed by our group.The linear regression curve,whose correlation for the data was 0.9995 and the residual was 2.8080,were obtained.The obtained correlation,residual, and the computation workload are all fit for the portable blood sugar analyzer.
文摘Let {Xt,t ≥ 1} be a moving average process defined by Xt = ∑^∞ k=0 αkξt-k, where {αk,k ≥ 0} is a sequence of real numbers and {ξt,-∞ 〈 t 〈 ∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {αk, k ≥ 0} which entail that {Xt, t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt, t ≥ 1} to a Gaussian process is studied. Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.
