剖析马氏链平稳分布的讲解——谈《应用随机过程》教学

通过平稳分布在Google搜索技术中的应用角度讲解马氏链的平稳分布的概念,并在此基础上对应用随机过程的教学做了粗浅的探讨.     

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.     

A class of Gaussian processes with fractional spectral measures

We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures σ (generalized spectral measures), and our focus here is on the case when the measure σ is a singular measure. We characterize the processes arising from σ when σ is in one of the classes of affine selfsimilar measures. Our analysis makes use of Kondratiev white noise spaces. With the use of a priori estimates and the Wick calculus, we extend and sharpen (see Theorem 7.1) earlier computations of Ito stochastic integration developed for the special case of stationary increment processes having absolutely continuous measures. We further obtain an associated Ito formula (see Theorem 8.1).     

Pullback attractors for a class of extremal solutions of the 3D Navier-Stokes system

In this paper we construct a dynamical process (in general, multivalued) generated by the set of solutions of an optimal control problem for the three-dimensional Navier-Stokes system. We prove the existence of a pullback attractor for such multivalued process. Also, we establish the existence of a uniform global attractor containing the pullback attractor. Moreover, under the unproved assumption that strong globally defined solutions of the three-dimensional Navier-Stokes system exist, which guaranties the existence of a global attractor for the corresponding multivalued semiflow, we show that the pullback attractor of the process coincides with the global attractor of the semiflow.     

Lp空间中随机变量的g-期望与条件g-期望

利用倒向随机微分方程的Lp解定义了Lp空间中随机变量g-期望与条件g-期望,扩张了g-期望与条件g-期望的定义空间;证明了用Lp解定义的g-期望与文[5]用算子连续扩张方法定义的一般g-期望的一致性,得到了Lp空间中随机变量的g-期望与条件g-期望的一些性质.     

Optimal control and dependence modeling of insurance portfolios with Lévy dynamics

In this paper we are interested in optimizing proportional reinsurance and investment policies in a multidimensional Lévy-driven insurance model. The criterion is that of maximizing exponential utility. Solving the classical Hamilton-Jacobi-Bellman equation yields that the optimal retention level keeps a constant amount of claims regardless of time and the company’s wealth level.A special feature of our construction is to allow for dependencies of the risk reserves in different business lines. Dependence is modeled via an Archimedean Lévy copula. We derive a sufficient and necessary condition for an Archimedean Lévy generator to create a multidimensional positive Lévy copula in arbitrary dimension.Based on these results we identify structure conditions for the generator and the Lévy measure of an Archimedean Lévy copula under which an insurance company reinsures a larger fraction of claims from one business line than from another.     

Resource allocation in dynamic PERT networks with finite capacity

This article models the resource allocation problem in dynamic PERT networks with finite capacity of concurrent projects (COnstant Number of Projects In Process (CONPIP)), where activity durations are independent random variables with exponential distributions, and the new projects are generated according to a Poisson process. The system is represented as a queuing network with finite concurrent projects, where each activity of a project is performed at a devoted service station with one server located in a node of the network. For modeling dynamic PERT networks with CONPIP, we first convert the network of queues into a stochastic network. Then, by constructing a proper finite-state continuous-time Markov model, a system of differential equations is created to solve and find the completion time distribution for any particular project. Finally, we propose a multi-objective model with three conflict objectives to optimally control the resources allocated to the servers, and apply the goal attainment method to solve a discrete-time approximation of the original multi-objective problem.     

关于求解随机用户均衡问题的截断拟牛顿型信赖域法研究

信赖域法是一种保证全局收敛性的优化算法,为避免Hessian矩阵的计算,基于拟牛顿校正公式构造了求解带线性等式约束的非线性规划问题的截断拟牛顿型信赖域法.首先给出了截断拟牛顿型信赖域法的构造过程及具体步骤;然后针对随机用户均衡模型中变量和约束的特点对算法进行了修正,并将多种拟牛顿校正公式下所得结果与牛顿型信赖域法的结果进行了比较,结果发现基于对称秩1校正公式的信赖域法更为合适.最后基于数值算例结果得到了一些在算法编程过程中的重要结论,对其它形式信赖域法的编程实现具有一定的参考意义.     

NA随机变量阵列的完全矩收敛性

利用NA随机变量的矩不等式和截尾方法,研究了NA随机变量阵列的完全矩收敛性,给出了证明NA随机变量阵列完全矩收敛性的一些充分条件.所得结果推广了已有文献关于NA随机变量的相应结果.     

带凹性生产成本运输问题的新随机规划模型及其求解

提出了一种新的能反映决策者满意度的随机变量序关系,并据此研究了随机不等式的确定性等价类,方法被称为满意度方法.最后将其应用于带凹性生产成本运输问题的求解中,并将方法与常用的机会约束方法进行比较,说明满意度法不仅合理可行,而且当决策者对约束条件的要求越高时,它所得最优值越优于机会约束法所得最优值.