概率性收敛

Convergence, convergence in probability, and convergence in distribution. And some sufficient and/or necessary conditions are also given.

收敛、统计依概率收敛的充要条件或充分条件，此外还讨论了几种收敛性之间的一些关系。

Classical limit theory includes the central limit theory, the law of large numbers, and the law of iterated logarithm etc.

经典的极限理论包括中心极限定理，大数律，重对数律等等，相对于收敛性来讲，就是依分布收敛，依概率收敛，和几乎必然收敛等等。

Limit theorems for the integration of function sequence with respect to weak convergence probability measure sequence are proved under the condition of the weak tight, which have been used to research the some convergence of expectant functional sequence,and a sufficient condition for the epi-convergence of expectant functional sequence is obtained.

提出了弱胎紧的概念，并在弱胎紧的条件下证明了函数序列关于弱收敛概率测度序列积分的极限定理，用其研究了期望泛函序列的若干收敛性，得到了期望泛函序列的、上图收敛的一个充分条件。

Since the concept of NA have a lot of applications in multivariate statistical analysis, reliability theory and percolation theory, various aspects of NA are significant and have been investigated by a host of scholars Fist, we give some Fuk-Nagaev type probability inequalities, moment inequalities of maximal partial sum for sequence of NA random variables, and some strong law of large numbers and complete convergence for sequence of NA random variables are obtained.

在本论文中我们对不要求强平稳或同分布的NA随机变量列进行了多方面的研究：首先对NA列建立了一组具有NA特点的关于最大部分和的Fuk-Nagaev型概率不等式及其关于某一类特定函数的矩不等式，它们在后续给出的极限定理的证明中发挥着重要作用；研究了具有不同分布的NA列的强收敛性，如对NA列建立了更一般条件下的Wittmann型强大数律及完全收敛性，同时也进一步改进了R。

According to disadvantage of AS that the speed low of convergentiss and easily entering the stagnation,improving the AS in some aspect by the way that importing pheromone windows that the value of pheromone cannot exceed the window,only deposit the pheromone on the edge that belongs to the iteration shortest solution path,releasing additional pheromone to the edge belongs to the so-far shortest solution path,judging the situation of convergent and to reinitialize pheromone,optimizing the solutions by local search procedure at the end of every iteration,modifying the transition probability by add some problem specific parameters and so on.

本文主要运用蚁群优化算法(Ant Colony Optimization，ACO)来求解VRP。针对蚁群算法收敛性比较差，易于停滞的缺陷，通过使用信息素窗口限制、信息素的最大最小值，只更新信息素迭代中最好解，增加了精英的蚂蚁，信息素重新初始化之前先判断出汇聚情况，在每次迭代过程中加入局部的搜索进行优化，在对蚁群算法进行了优化时考虑选择概率当中加入与问题的相关参数等措施，从而使蚁群算法的收敛性得到大大提高，避免了算法的停滞现象。

And then obtained under some conditions of probability are some sufficient conditions for moment complete convergence for independent non-identically distributed random elements in a separable Banach space which are stochastically bounded by a positive random variable.

文章在随机元序列随机有界于某非负随机变量的条件下，引入慢变化函数l和选定的函数类S，在一定的概率性条件下，得到B值独立不同分布随机元序列矩完全收敛性的充分条件，推广了有关文献的结果。

The asymptotic unbias edness and the strong consistency and rate of convergence under given conditions are obtained.

在测度弱收敛的意义下，研究了一般概率测度μ的核估计μn，得到了它的渐近无偏性、强相合性及在给定条件下的收敛速度。

Stochastic convex programming; Monte Carlo methods; Financial optimization; Convergence with probability one; Optimality condition; Monte Carlo penalty function methods; Nonsmooth optimization; Directional derivative; Subdifferential; Confident interval; Conditional Value-at-Risk; Optimal reinsurance

基础科学，数学，运筹学随机凸规划； Monte Carlo方法；金融优化；以概率1收敛；最优性条件； Monte Carlo罚函数法；非光滑优化；方向导数；次微分；置信区间；条件风险价值；最优再保险

Substituting them into the optimal weighted fusion Wiener filter of the AR signals, a self-turning weighted fusion Wiener filter is presenced, which convergence to the optimal weighed fusion Wiener filter, so that it has the asymptotic optimality.

将它们代入最优加权融合AR信号Wiener滤波器，提出一种自校正加权融合Wiener滤波器。它们以概率1收敛于最优融合Wiener滤波器，因而具有渐近最优性。

Firstly, an empirical approximation model of stochastic programming is obtained by replacing the probability measure of original program with empirical probability measure. Sequentially, the constrained stochastic programming is transformed into an equivalent unconstrained stochastic programming. Finally, using the epi-convergence theory, the almost everywhere upper semiconvergence of optimal solution set of empirical approximations for stochastic programming is obtained.

首先通过经验概率测度替代初始规划的概率测度得到随机规划的经验逼近模型，然后将带有约束的随机规划问题转化成与其等价的无约束的随机规划问题，最后利用上图收敛性理论，给出了随机规划经验逼近最优解集的几乎处处上半收敛性。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。