Maximizing an interval order on compact subsets of its domain

Maximal elements of a binary relation on compact subsets of a metric space define a choice function. An infinite extension of transitivity is necessary and sufficient for such a choice function to be nonempty-valued and path independent (or satisfy the outcast axiom). An infinite extension of acyclicity is necessary and sufficient for the choice function to have nonempty values provided the underlying relation is an interval order.     

Two methods for minimizing convex functions in a class of nonconvex sets

The conditional gradient method and the steepest descent method, which are conventionally used for solving convex programming problems, are extended to the case where the feasible set is the set-theoretic difference between a convex set and the union of several convex sets. Iterative algorithms are proposed, and their convergence is examined.     

Conditional independence,conditional mixing and conditional association

Some properties of conditionally independent random variables are studied. Conditional versions of generalized Borel-Cantelli lemma, generalized Kolmogorov’s inequality and generalized Hájek-Rényi inequality are proved. As applications, a conditional version of the strong law of large numbers for conditionally independent random variables and a conditional version of the Kolmogorov’s strong law of large numbers for conditionally independent random variables with identical conditional distributions are obtained. The notions of conditional strong mixing and conditional association for a sequence of random variables are introduced. Some covariance inequalities and a central limit theorem for such sequences are mentioned.     

M-estimation in nonparametric regression under strong dependence and infinite variance

A robust local linear regression smoothing estimator for a nonparametric regression model with heavy-tailed dependent errors is considered in this paper. Under certain regularity conditions, the weak consistency and asymptotic distribution of the proposed estimators are obtained. If the errors are short-range dependent, then the limiting distribution of the estimator is normal. If the data are long-range dependent, then the limiting distribution of the estimator is a stable distribution.     

Stable sets, corner polyhedra and the Chvátal closure

We consider the edge formulation of the stable set problem. We characterize its corner polyhedron, i.e. the convex hull of the points satisfying all the constraints except the non-negativity of the basic variables. We show that the non-trivial inequalities necessary to describe this polyhedron can be derived from one row of the simplex tableau as fractional Gomory cuts. It follows that the split closure is not stronger than the Chvátal closure for the edge relaxation of the stable set problem.     

不同模型下ES风险度量的计算

给出当金融资产遵从几何布朗运动时期望损失的计算。当金融资产价格的对数收益率服从均值方程为ARMA模型,方差方程为GARCH(s,n)模型,而均值修正后的收益率分别服从正态分布、t分布和GED分布时,给出了期望损失的计算。     

任意B值随机变量序列关于条件期望的一类强极限定理

利用随机变量的截尾方法和条件三级数定理,研究任意B值随机变量序列的极限性质,得到了一类关于条件期望的强极限定理和鞅差序列收敛定理,推广了与此相应的一些结果和若干经典的强大数定律.     

多服务台排队系统的组装策略

本文讨论了(e,d)-策略多重休假的M/M/c排队,这是—个M/M/c-e和M/M/c排队的“组装”策略,为系统设计提供更大的灵活性．使用拟生灭过程方法,给出了稳态队长分布．进一步地,利用条件Erlang分布的一些有趣的性质,给出了等待时间分布的简洁表达式．最后,得到稳态指标的条件随机分解结果．     

模糊残缺判断矩阵的修补

模糊判断矩阵是决策者在决策中所提供的一种重要的偏好信息,然而专家所给出的判断矩阵可能是带有残缺的.给出了模糊残缺判断矩阵中残存元素的极大一致独立组、残存元素组导出图、残缺矩阵的可接受性概念,并讨论了模糊残缺判断矩阵的极大一致独立组的导出图是树的条件,进而说明n阶模糊残缺矩阵中n-1个元素所导出的图是n阶树的话,模糊残缺判断矩阵即为可接受的.最后给出了一个可接受的残缺判断矩阵修补的算例.