Quasi-sure Product Variation of Two-parameter Smooth Martingales on the Wiener Space

In this paper, we prove that the process of product variation of a two-parameter smooth martingale admits an ∞ modification, which can be constructed as the quasi-sure limit of sum of the corresponding product variation.     

Sample-path optimality and variance-maximization for Markov decision processes

This paper studies both the average sample-path reward (ASPR) criterion and the limiting average variance criterion for denumerable discrete-time Markov decision processes. The rewards may have neither upper nor lower bounds. We give sufficient conditions on the system’s primitive data and under which we prove the existence of ASPR-optimal stationary policies and variance optimal policies. Our conditions are weaker than those in the previous literature. Moreover, our results are illustrated by a controlled queueing system. Research partially supported by the Natural Science Foundation of Guangdong Province (Grant No: 06025063) and the Natural Science Foundation of China (Grant No: 10626021).     

未确知集

分析了模糊集与R ough集两种不确定性集合的异同,指出模糊集中存在的不足和缺陷,在此基础上定义一种新的不确定性集合称作未确知集.在未确知集中模糊集的不足与缺陷得到弥补与修正,并且未确知集具有普通集合的含义.通过分析未确知集与模糊集的相同点及本质区别来论证未确知集存在与值得研究的价值.最后例举了常用的未确知隶属函数的构造方法.     

基于Dirichlet分布有限混合模型的Bayes聚类

本文基于Dirichlet分布有限混合模型,提出了一种用于成分数据的Bayes聚类方法.采用EM算法获得模型参数的估计,用BIC准则确定类数,用类似于Bayes判别的方法对各观测分类.推导了计算公式,编写出程序.模拟研究结果表明,本文提出的方法有较好的聚类效果.     

A discrete hierarchical model of intra-specific competition

A discrete hierarchical model with either age, size, or stage structure is derived. The resulting scalar equation for total population level is then used to study contest and scramble intra-specific competition. It is shown how equilibrium levels and resilience are related for the two different competition situations. In particular, scramble competition yields a higher population level while contest competition is more resilient if the uptake rate as a function of resource density is concave down. The conclusions are reversed if the uptake rate is concave up.     

First Exit Times for Ordinary and Compound Poisson Processes with Non-linear Boundaries

Distributions of the first-exit times from a region with concave upper boundary are discussed for ordinary and compound Poisson processes. Explicit formulae are developed for the case of ordinary Poisson processes. Recursive formulae are given for the compound Poisson case, where the jumps are positive, having discrete or continuous distributions with finite means. Applications to sequential point estimation and insurance are illustrated.      

A global attractivity criterion for nonlinear non-autonomous difference equations

We establish a discrete version of the celebrated Yorke and Wright 3/2-stability criterion for a family of strongly nonlinear non-autonomous difference equations of the form xn+1=xn+anfn(xn,…,xn−k).     

Unconditional Schauder decompositions and stopping times in the Lebesgue-Bochner spaces

We extend Troitsky's study of martingales in Banach lattices to include stopping times. Results from the theory of unconditional Schauder decompositions and multipliers are used to derive an optional stopping theorem for unbounded stopping times. We also apply these techniques to convergent nets of stopped processes, as well as to unconditional Schauder decompositions in vector-valued Lp-spaces (1<p<∞).     

Kerr-Newman黑洞的谐振子模型及量子面积谱

利用Kerr-Newman黑洞的质量M，电量Q，角动量J和它们各自的对偶量，π_M,π_Q,π_J,构成的六维相空间，通过规范变换，首先建立黑洞的简谐振子模型；再利用该模型进一步研究Kerr-Newman黑洞的量子面积谱. 关键词： 黑洞 规范变换 简谐振子模型 量子面积谱