Joint Limit Distributions of Exceedances Point Processes and Partial Sums of Gaussian Vector Sequence

In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence （centered at the sample mean） converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.

Limit Distributions for Generalized Jirina Processes with Immigration

A relationship between continuous state population-size-dependent branching （CSDB） processes with or without immigration and discrete state population-size-dependent branching （DSDB） processes with or without immigration is established via the representation of the former. Based on this relationship, some limiting distributions of CSDB processes with or without immigration are obtained.

CLASSICAL LIMITS FOR THE COEFFICIENT OF VARIATION FOR THE NORMAL DISTRIBUTION

The exact classical limits for the coefficient of variation c for the normal distribution are derived. The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineering needs. Using Odeh and Owen's computational method and Brent's algorithm, the tables for the r-upper exact classical limits of coefficient of variation for normal distribution are calculated for the different confidence coefficient y, the sample size n=1(1)30,40,60,120, the sample coefficient of variation c=0.01(0.01)0.20. It is shown that if n<8,c<0.20, then the V -upper exact classical limits cu for c are slightly higher than the exact fiducial limits cu,F for c if. n>8, c<0.02,then cu-cu,f<5x10-6

基于动态调节下垂曲线的光伏逆变器两阶段协调控制策略

在分布式光伏高渗透的有源配电网中,常规集中、局部电压控制已无法经济有效地解决电压越限、波动问题。为此提出光伏逆变器集中-局部电压两阶段控制策略,局部控制曲线采用多曲线节点灵活可调的改进无功-电压(Q-V)下垂曲线。集中控制阶段以电压控制成本与电压越限条件风险价值的加权和最小为目标函数,利用分布鲁棒优化算法和模型预测控制算法考虑光伏出力预测不确定性,对各光伏逆变器的有功功率削减量参考值和Q-V下垂曲线进行分钟级全局优化设置和调节;局部控制阶段根据Q-V下垂曲线和实时测量的节点电压,动态调整光伏逆变器无功出力。采用改进的IEEE 37节点配电系统进行仿真,结果表明:所提控制策略不仅能够集中、最优地协调各光伏逆变器的有功功率削减量和无功出力,避免电压越限,还能在局部控制阶段利用集中优化后的Q-V下垂曲线使电压波动降低40.56%,满足配电网运营商对电压控制经济性和鲁棒性的不同需求。

First exit distribution and path continuity of Hunt processes

This paper gives a characterization of a Hunt process path by the first exit left limit distribution. It is also showed that if the first exit left limit distribution leaving any ball from the center is a uniform distribution on the sphere, then the Levy Processes are a scaled Brownian motion.

Almost sure limit theorem for the maximum of a class of quasi-stationary sequences

This paper investigates the problem of almost sure limit theorem for the maximum of quasi-stationary sequence based on the result of Turkman and Walker. We prove an almost sure limit theorem for the maximum of a class of quasi-stationary sequence under weak dependence conditions of D （uk, un） and αtm,ln = 0 （（log log n）-（1＋ε））.

Climatic envelope of evergreen sclerophyllous oaks and their present distribution in the eastern Himalaya and Hengduan Mountains

Evergreen sclerophyllous oaks （the E.S. oaks, Quercus section Heterobalanus） are the dominant species of the local ecosystem in the eastern Himalaya and the Hengduan Mountains, southwest China. In this study, we document the climatic envelope of the seven E.S. oak species and examine the relationships between climate and their distribution. This was done using a principal components analysis （PCA） and multiple regression analysis （MRA） of nine climatic indices. The main climatic envelope of the E.S. oaks were： mean temperature of the warmest month （MTW）= 12.0-19.5℃, warmth index （WI） = 33.2-88.9℃ month, annual biotemperature （BT）=-6.9- -0.3 ℃, coldness index （CI）=-30.4- -10.1 ℃ month, mean temperature of the coldest month （MTC）=-3.7-3.0℃ and annual precipitation （AP）=701-897 mm at the lower limits; and MTW=8.3-16.1℃, WI=15.7-59.1℃ month, BT=3.6-8.9℃, CI=-55.4-19.3℃ month, MTC=8.3-16.1 ℃ and AP=610-811 mm at the upper limits. The climatic range of the E.S. oaks is wide and includes two climatic zones, the cool-temperature zone and the subpolar zone. The PCA and MRA results suggest that the thermal climate plays a major role and precipitation plays a secondary role in controlling the large-scale distribution of the E.S. oaks, except Quercus monimotricha. In thermal regimes, BT and/or MTW are most important for both lower and upper limits of the E.S. oaks. Furthermore, our results indicate that the upper distribution limits of the E.S. oaks are less determined by low temperatures and their duration （CI） than by other factors.

不同碳交易配额分配方法下的鲁棒减排运作策略研究

本文结合当前碳交易配额分配方式多样化和需求分布信息不确定的现象,研究历史法和基准线碳配额分配方式下企业的鲁棒减排运作策略。通过构建和求解两种碳配额政策下企业减排运作决策的鲁棒优化模型,本文给出不同碳配额政策下企业进行减排投资的必要条件。不同碳配额政策下最优减排运作决策、经济和环境绩效的对比分析揭示了两种碳配额分配方法对最差分布下企业利润和碳排放量的影响。通过理论分析结合数值实验发现,相同减排水平下,基准线法碳配额下的最优生产量高于历史法碳配额下的最优生产量;虽然基准线法碳配额下的碳排放总量高于历史法碳配额下的值,但单位产品碳排放量在一定条件下却可以低于历史法碳配额下的值。用基准线法设定碳配额能充分调动企业的生产积极性,政府可以通过调整基准线法碳配额的数值使企业实现高利润低排放,从而实现经济和环境协调发展的目标。

The CUSUM statistic of change point under NA sequences

In this paper,we investigate the CUSUM statistic of change point under the neg-atively associated(NA)sequences.By establishing the consistency estimators for mean and covariance functions respectively,the limit distribution of the CUSUM statistic is proved to be a standard Brownian bridge,which extends the results obtained under the case of an indepen-dent normal sample and the moving average processes.Finally,the finite sample properties of the CUSUM statistic are given to show the efficiency of the method by simulation studies and an application on a real data analysis.

A THEOREM ON THE CONVERGENCE OF SUMS OF INDEPENDENT RANDOM VARIABLES

Let Sigma (infinity)(n=1) X-n be a series of independent random variables with at least one non-degenerate X-n, and let F-n be the distribution function of its partial sums S-n = Sigma (n)(k=1) X-k. Motivated by Hildebrand's work in [1], the authors investigate the a.s. convergence of Sigma (infinity)(n=1) X-n under a hypothesis that Sigma (infinity)(n=1) rho (X-n, c(n)) = infinity whener Sigma (infinity)(n=1) c(n) diverges, where the notation rho (X,c) denotes the Levy distance between the random variable X and the constant c. The principal result of this paper shows that the hypothesis is the condition under which the convergence of F-n(x(0)) with the limit value 0 < L-0 < 1, together with the essential convergence of Sigma (infinity)(n=1) X-n, is both sufficient and necessary in order for the series Sigma (infinity)(n=1) X-n to a.s. coverage. Moreover, if the essential convergence of Sigma (infinity)(n=1) X-n is strengthened to limsup(n=infinity) P(\S-n\ < K) = 1 for some K > 0, the hypothesis is already equivalent to the a.s. convergence of Sigma (infinity)(n=1) X-n. Here they have not only founded a very general limit theorem, but improved the related result in Hildebrand([1]) as well.

Asymptotic inference for AR(1) panel data

A general asymptotic theory is given for the panel data AR(1) model with time series independent in different cross sections. The theory covers the cases of stationary process, local to unity process, unit root process, mildly integrated, mildly explosive and explosive processes. It is assumed that the cross-sectional dimension and time-series dimension are respectively N and T. The results in this paper illustrate that whichever the process is, with an appropriate regularization, the least squares estimator of the autoregressive coefficient converges in distribution to a normal distribution with rate at least O(N-1/3). Since the variance is the key to characterize the normal distribution, it is important to discuss the variance of the least squares estimator. We will show that when the autoregressive coefficient ρ satisfies |ρ| < 1, the variance declines at the rate O((NT)-1), while the rate changes to O(N^(-1) T^(-2)) when ρ = 1 and O(N^(-1)ρ^(-2 T+4)) when |ρ| > 1. ρ = 1 is the critical point where the convergence rate changes radically. The transition process is studied by assuming ρ depending on T and going to 1. An interesting phenomenon discovered in this paper is that, in the explosive case, the least squares estimator of the autoregressive coefficient has a standard normal limiting distribution in the panel data case while it may not has a limiting distribution in the univariate time series case.

DUAL RANDOM MODEL OF INCREASING LIFE INSURANCE FOR MULTIPLE-LIFE STATUS

In this paper the dual random model of increasing life insurance for multiple-life status is discussed.The mth moment of the present value of benefits are calculated and the respective expressions of the moments under joint life status or last- survivor status are presented.Fur-thermore,the limiting distribution of average cost of a portfolio of increasing life insurance for multiple-life status is studied.

THE LIMITING DISTRIBUTIONS OF SOME SUBCLASSES OF THE GENERALIZED NON-CENTRAL t-DISTRIBUTION

A general theorem on the limiting distribution of the generalized t-distribution is obtained,many applications of this theorem to some subclasses of elliptically contoured distributions in cluding multivariate normal and multivariate t distributions are discussed.Further,their limiting distributions by density function are derived.

The convergence on spectrum of sample covariance matrices for information-plus-noise type data

In this paper,we consider the limiting spectral distribution of the information-plus-noise type sample covariance matrices Cn=1/N（Rn＋σXn）（Rn＋σXn）,under the assumption that the entries of Xn are independent but non-identically distributed random variables.It is proved that,almost surely,the empirical spectral distribution of Cn converges weakly to a non-random distribution whose Stieltjes transform satisfies a certain equation.Our result extends the previous one with the entries of Xn are i.i.d.random varibles to a more general case.The proof of the result mainly employs the Stein equation and the cumulant expansion formula of independent random variables.

DISTRIBUTIONS OF LIMIT CYCLES FOR POLYNOMIAL VECTOR FIELDS (P_2, Q_3)

The distributions of limit cycles of cubic vector fields (P2, Q3) are considered in this paper, where P2 and Q3 are polynomials of x and y of order two and three, respectively. It is possibly seven different distributions of limit cycles given in [1]. We now prove that in which three kinds of distributions are impossible and other four kinds all can be realized by concrete vector fields of (P2,Q3). Some related results are also given.

On Optimal Ordering of Service Parameters of a Coxian Queueing Model with Three Phases

We analyze a Coxian stochastic queueing model with three phases. The Kolmogorov equations of this model are constructed, and limit probabilities and the stationary probabilities of customer numbers in the system are found. The performance measures of this model are obtained and in addition the optimal order of service parameters is given with a theorem by obtaining the loss probabilities of customers in the system. That is, putting the greatest service parameter at first phase and the second greatest service parameter at second phase and the smallest service parameter at third phase makes the loss probability and means waiting time minimum. We also give the loss probability in terms of mean waiting time in the system. is the transition probability from j-th phase?to??phase . In this manner while and this system turns into queueing model and while the system turns into Cox(2) queueing model. In addition, loss probabilities are graphically given in a 3D graph for corresponding system parameters and phase transient probabilities. Finally it is shown with a numeric example that this theorem holds.

Exploring the impact of a coordinated variable speed limit control on congestion distribution in freeway

Over the past few decades, urban freeway congestion has been highly recognized as a serious and worsening traffic problem in the world. To relieve freeway congestion, several active traffic and demand management （ATDM） methods have been developed. Among them, variable speed limit （VSL） aims at regulating freeway mainline flow upstream to meet existing capacity and to harmonize vehicle speed. However, congestion may still be inevitable even with VSL implemented due to extremely high demand in actual practice. This study modified an existing VSL strategy by adding a new local constraint to suggest an achievable speed limit during the control period. As a queue is a product of the congestion phenomenon in freeway, the incentives of a queue build-up in the applied coordinated VSL control situation were analyzed. Considering a congestion occurrence （a queue build-up） characterized by a sudden and sharp speed drop, speed contours were utilized to demonstrate the congestion distribution over a whole freeway network in various sce- narios. Finally, congestion distributions found in both VSL control and non-VS control situations for various scenarios were investigated to explore the impact of the applied coordinated VSL control on the congestion distribution. An authentic stretch of V^hitemud Drive （I~~ID）, an urban freeway corridor in Edmonton, Alberta, Canada, was employed to implement this modified coordinated VSL control strategy; and a calibrated micro-simu- lation VISSIM model （model functions） was applied as the substitute of the real-world traffic system to test the above mentioned performance. The exploration task in this study can lay the groundwork for future research on how to improve the presented VSL control strategy for achieving the congestion mitigation effect on freeway.

Bifurcations of Limit Cycles in a Z_4-Equivariant Quintic Planar Vector Field

In this paper, a Z4-equivariant quintic planar vector field is studied. The Hopf bifurcation method and polycycle bifurcation method are combined to study the limit cycles bifurcated from the compounded cycle with 4 hyperbolic saddle points. It is found that this special quintic planar polynomial system has at least four large limit cycles which surround all singular points. By applying the double homoclinic loops bifurcation method and Hopf bifurcation method, we conclude that 28 limit cycles with two different configurations exist in this special planar polynomial system. The results acquired in this paper are useful for studying the weakened 16th Hilbert＇s Problem.

On eigenvalues of a high-dimensional Kendall's rank correlation matrix with dependence

In this paper,we investigate the limiting spectral distribution of a high-dimensional Kendall’s rank correlation matrix.The underlying population is allowed to have a general dependence structure.The result no longer follows the generalized Marcenko-Pastur law,which is brand new.It is the first result on rank correlation matrices with dependence.As applications,we study Kendall’s rank correlation matrix for multivariate normal distributions with a general covariance matrix.From these results,we further gain insights into Kendall’s rank correlation matrix and its connections with the sample covariance/correlation matrix.

On the Longest Length of Consecutive Integers

Choose m numbers from the set {1,2,... ,n} at random without replacement. In this paper we first establish the limiting distribution of the longest length of consecutive integers and then apply the result to test randomness of selecting numbers without replacement.