离散偏序集上的最优停点和最优策略

本文将[1]中定理1的一致有界性条件减弱到A~ 条件并首次得到了偏序集上最优停点和最优策略的充要条件.     

线性回归模型中的后验影响函数

本文对线性回归模型定义了后验影响函数;针对已有的先验信息的三种不同情况给出了它的分解式,讨论了其优良性;指出强影响点、异常点、高杠杆点的内在联系,讨论了上述三种点的探测方法。     

由停时所确定的事件域

本文对于Markov过程的自然滤子详细讨论了停时前以及严格停时前的事件域,并给出介于首中时和逃逸时之间的停时的刻画。     

某些Banach空间的有限阶光滑点和强光滑点

本文给出ｌ∞（Ｘ）以及Ｌ１（ｌ１（Ｘ），ｙ），Ｌ（Ｘ，ｌ∞（Ｙ））和Ｌ（Ｘ，ｃｏ（Ｙ））的单位球的有限阶光滑点和强光滑点的充要条件，这是Ｘ和Ｙ都是任意的Ｂａｎａｃｈ空间，特别地，本文给出这些空间的单位球的光滑点和强光滑点的充要条件。     

二元函数微分中值定理中值点的分析性质

讨论二元函数微分中值定理中值点的连续性及可导性问题,给出二元函数微分中值定理中值点连续及偏导数存在的充分务停,同时给出计算其偏导数的公式。     

一类非对称的“跳-停”奇异型随机控制

研究了一类带停时的非对称的奇异型随机控制的折扣问题,不论是从受控状态过程还是从费用函数均推广为较一般的情形,得到"跳-停"策略是其最优控制策略,并给出了"跳-停"策略存在的条件、最优费用函数以及控制方法,所得的结论在实际中有较深的应用背景。     

位置参数变点估计的强收敛速度

对至多一个变点的位置参数变点模型,文中在运用滑窗方法给出了检测变点存在性的U-统计量基础上,进一步研究了变点估计量的强相合性和强收敛速度.     

赋Orlicz范数的Musielak-Orlicz空间的光滑点与强光滑点(英)

给出赋Ｏｒｌｉｃｚ范数的Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ函数空间中光滑点、光滑性、强（很）光滑点和强（很）光滑性的充 分必要条件．     

树上乘积自映射周期点集的局部度量稳定性

本文研究了树上乘积自映射的性质,给出了它在周期点集上等度连续的5个充要条件。     

在折现率大于零的情况下,具有完成时间和残值不确定性的R&D项目的投资策略

利用随机停时理论 ,考虑 R&D项目的连续投资策略 .在折现率大于零的情况下 ,给出了具有建设期和残值的不确定性的 R&D投资模型、放弃 R&D项目投资的临界值和最优决策规则 ,并讨论参数对临界值的影响 .也进一步验证了随机停时理论和实物期权理论在投资决策分析中的一致性 .     

On stopping points in the plane that lie on a unique optional increasing path

Given a stopping point in the plane, is there an optional increasing path that passes through the stopping point with probability one? The commutation Hypothesis F4 of Cairoli and Walsh was known to be a sufficient condition in continuous time, and we prove that the conditional qualitative independence Hypothesis CQI of Krengel and Sucheston is in fact necessary and sufficient. Rather surprisingly, certain stopping points may lie on a unique optional increasing path, even when the two-parameter nitration is the natural filtration ot a Rrownian sheet. In the construction of these examples, we prove a result of independent interest, namely that the solutions to certain random differentia! equations are optional increasing paths     

Stopping rules,permutation invariance and sufficiency principle

In the context of sequential (point as well as interval) estimation, a general formulation of permutation-invariant stopping rules is considered. These stopping rules lead to savings in the ASN at the cost of some elevation of the associated risk—a phenomenon which may be attributed to the violation of the sufficiency principle. For the (point and interval) sequential estimation of the mean of a normal distribution, it is shown that such permutation-invariant stopping rules may lead to a substantial saving in the ASN with only a small increase in the associated risk.Work partially supported by (i) Office of Naval Research, Contract Number N00014-85-K-0548, and (ii) Office of Naval Research, Contract Number N00014-83-K-0387.     

A stopping game in a stochastic and fuzzy environment

A zero-sum stopping game for a sequence of fuzzy-valued random variables is discussed. The fuzzy random variables are estimated by probabilistic expectation and fuzzy expectation. A saddle point is given for the stopping game.     

中止规则的平均延迟时间及其应用

本文以平均延迟时间为度量，对适用于连续抽样方案的四种中止规则，即规则［Ｓ］，［Ｒ］，［Ｎ，ｃ］及［Ｒ，ｄ］的中止“速度”进行了比较。结果表明：［Ｒ］优于［Ｓ］，而［Ｎ，ｃ］与［Ｒ，ｄ］均优于［Ｒ］。这些结论及方法可被用来适当地选择中止规则，以提高连续型生产的质量控制水平     

Approaches to multistage one-shot decision making

In this research, multistage one-shot decision making under uncertainty is studied. In such a decision problem, a decision maker has one and only one chance to make a decision at each stage with possibilistic information. Based on the one-shot decision theory, approaches to multistage one-shot decision making are proposed. In the proposed approach, a decision maker chooses one state amongst all the states according to his/her attitude about satisfaction and possibility at each stage. The payoff at each stage is associated with the focus points at the succeeding stages. Based on the selected states (focus points), the sequence of optimal decisions is determined by dynamic programming. The proposed method is a fundamental alternative for multistage decision making under uncertainty because it is scenario-based instead of lottery-based as in the other existing methods. The one-shot optimal stopping problem is analyzed where a decision maker has only one chance to determine stopping or continuing at each stage. The theoretical results have been obtained.     

Strong Markov Properties for Markov Random Fields

Markov properties and strong Markov properties for random fields are defined and discussed. Special attention is given to those defined by I. V. Evstigneev. The strong Markov nature of Markov random fields with respect to random domains such as [0, L], where L is a multidimensional extension of a stopping time, is explored. A special case of this extension is shown to generalize a result of Merzbach and Nualart for point processes. As an additional example, Evstigneev's Markov and strong Markov properties are considered for independent increment jump processes.     

Optimal stopping for extremal processes

For an extremal process (Z_t)_t the optimal stopping problem for X_t = f(Z_t)?g(t) gives the continuous time analogue of the optimal stopping problem for max{Y₁,…,Y_k}?c_k where Y₁, Y₂,… are i.i.d. For the continuous time problem we derive optimal stopping times in explicit form and also show that the optimal stopping boundary is the limit of the optimal stopping boundaries for suitably standardized discrete problems.     

两指标点过程的停止及σ-域

本文给出两指标点过程的跳线刻划、停止方法,论述了跳线的可测性及点过程有关的σ-域的结构和特征。     

Hit-and-run algorithms for the identification of nonredundant linear inequalities

Two probabilistic hit-and-run algorithms are presented to detect nonredundant constraints in a full dimensional system of linear inequalities. The algorithms proceed by generating a random sequence of interior points whose limiting distribution is uniform, and by searching for a nonredundant constraint in the direction of a random vector from each point in the sequence. In the hypersphere directions algorithm the direction vector is drawn from a uniform distribution on a hypersphere. In the computationally superior coordinate directions algorithm a search is carried out along one of the coordinate vectors. The algorithms are terminated through the use of a Bayesian stopping rule. Computational experience with the algorithms and the stopping rule will be reported.