马尔可夫跳过程的弱收敛

本文通过马尔可夫跳过程的嵌入链的收敛性表征马尔可夫跳过程的弱收敛。特别,得到了用无穷小特征表征的时齐马尔可夫跳过程的收敛定理及时齐马尔可夫跳过程的离散逼近。     

有趣的青蛙对称跳

地面上有A、B、C三点,一只青蛙位于地面上距离A点为0.27米的P点.青蛙第一步从P点跳到关于A的对称点P1,我们把这个动作说成是青蛙从P点关于A点的“对称跳”;第二步从P1点出发对B点作对称跳到达P2;第三步从P2点出发对C点作对称跳到达P3;第四步从P3再对A作对称跳到达P4;…,按这种方式一直跳下去,若青蛙第2005步对称跳之后到达P2005,问此点与出发点P的距离为多少米?图1如图2,从P点跳过两次之后到达P2点,相当于按向量PP2作了一次平移,而PP2=2AB,类似地,第三次和第四次两次跳相当于按向量2CA做平移,第五次和第六次跳相当于按向量2BC…     

带跳单指标模型的半参数跳点检测估计

单指标模型是统计学中常用的维数约减模型.在实际应用中,连接函数可能有奇异点,包括某些未知位置上有跳点和某些相关过程的结构变点.检测这些奇异点对于系数估计和了解结构改变非常重要.本文基于精细最小平均条件方差估计和函数二阶导数的零穿越性质,提出一个跳点检测方法,然后利用检测出的跳点给出参数向量和连接函数的半参数跳点检测估计量,并讨论程序参数的选择.在较弱的假设条件下,本文建立跳点检测程序和所提估计量的大样本性质.数值模拟和实例分析验证了所提方法在有限样本下的表现.     

一般状态空间跳过程的正则性

给出了一般状态空间正则跳过程的定义,通过跳过程的比较定理,证明了一般状态空间跳过程正则性的两个等价条件:矩条件和漂移条件.     

跳过程唯一性的一个问题

本文从跳过程随机可比的必要条件出发，证明某种意义上的控制q对的正则性蕴含被控制q对决定唯一的跳过程．     

跳过程的Malliavin分析

本文讨论一类跳过程的分布的密度的存在性.用 Malliavin 分析技巧和鞅方法证明了一类跳过程的分布有 L~P 可积的密度.所得结果是新的,并指出了[1]中的错误.     

具有一般跳幅度分布的跳扩散模型下永久公司债券的定价

在公司资产价值演化服从具有一般跳幅度分布的跳扩散模型下,采用结构化方法研究具有无限到期日公司债券的定价问题,通过微分方程的方法和无套利原理获得了公司债券,股东权益和公司总价值的定价表达式以及最佳违约边界的表达式.     

跳过程的Malliavin分析

本文讨论一类跳过程的分布的密度的存在性。用Malliavin分析技巧和鞅方法证明了一类跳过程的分布有L~p可积的密度。所得结果是新的,并指出了[1]中的错误。     

跳过程随机可比的充要条件

本文研究跳过程的随机可比性·基于文献［２］和［３］,证明两个跳过程随机可比的充要条件是其ｑ对可比·同时,改进了［６］中唯一性问题的结果     

沪深300指数日内跳的Hausman检验

本文采用半鞅过程的双重次方变差和多重次方变差构造的跳检验统计量,对沪深300指数进行日内跳检验。检验结果表明,沪深300指数多于1/3的交易日有跳发生,跳发生的概率在不同交易时段并不均匀,并表现出一定的持续性。计算结果表明,跳二次变差在二次变差中占的比例高达32.48%,是二次变差的重要组成部分。     

二次曲面和平面位置关系的判式

在解析几何中有二次曲线与直线位置关系的讨论、二次曲面与直线位置关系的讨论,而二次曲面与平面相关位置关系的探讨较少.本文给出二次曲面a11x2+a22y2+a33z2+2a12xy+2a13xz+2a23yz+2a14x+2a24y+2a34z+a44=0(1)和平面Ax+By+Cz+D=0(2)的相对位置的判别式Δ=a11a12a13a14Aa21a22a23a24Ba31a32a33a34Ca41a42a43a44DA B C D0(aij=aji).(3)并证明了:若Δ>0,则二次曲面(1)与平面(2)相交;若Δ=0,则(1)和(2)相切;若Δ<0,则(1)和(2)相离.     

Subspaces and quotients of Banach spaces with shrinking unconditional bases

The main result is that a separable Banach space with the weak* unconditional tree property is isomorphic to a subspace as well as a quotient of a Banach space with a shrinking unconditional basis. A consequence of this is that a Banach space is isomorphic to a subspace of a space with a shrinking unconditional basis if and only if it is isomorphic to a quotient of a space with a shrinking unconditional basis, which solves a problem dating to the 1970s. The proof of the main result also yields that a uniformly convex space with the unconditional tree property is isomorphic to a subspace as well as a quotient of a uniformly convex space with an unconditional finite dimensional decomposition.     

Scalarization of Henig Proper Efficient Points in a Normed Space

In a general normed space equipped with the order induced by a closed convex cone with a base, using a family of continuous monotone Minkowski functionals and a family of continuous norms, we obtain scalar characterizations of Henig proper efficient points of a general set and a bounded set, respectively. Moreover, we give a scalar characterization of a superefficient point of a set in a normed space equipped with the order induced by a closed convex cone with a bounded base.     

Two questions on semi-clean group rings

It was proved in [4] that every group ring of a torsion abelian group over a commutative local ring is a semi-clean ring. It was asked in [4] whether every group ring of a torsion abelian group over a commutative clean ring is a semi-clean ring and whether every group ring of a torsion abelian group over a commutative semi-clean ring is a semi-clean ring. In this paper, we give a positive answer to question 1 and a negative answer to question 2.     

A generalized duality and applications

The aim of this paper is to present a nonconvex duality with a zero gap and its connection with convex duality. Since a convex program can be regarded as a particular case of convex maximization over a convex set, a nonconvex duality can be regarded as a generalization of convex duality. The generalized duality can be obtained on the basis of convex duality and minimax theorems. The duality with a zero gap can be extended to a more general nonconvex problems such as a quasiconvex maximization over a general nonconvex set or a general minimization over the complement of a convex set. Several applications are given.On leave from the Institute of Mathematics, Hanoi, Vietnam.     

图的分数k-因子

给定图G=(V,E).设a和b是两个非负整数.fE→［0,1］是一个函数.如果     

Inventory replenishment model: lot sizing versus just-in-time delivery

Motivated by a practical industrial problem where a manufacturer stipulates a minimum order from each buyer but where a local dealer promises the buyer a just-in-time delivery with a slightly higher unit cost, this paper uses a dynamic lot-sizing model with a stepwise cargo cost function and a minimum order amount constraint to help the buyer select the supplier with minimum total cost.     

Invariant diffusion processes under Lie group actions

We study a decomposition of a diffusion process in a manifold that is invariant under the action of a Lie group. As applications, we consider a diffusion process in a Euclidean space that is invariant under translations in a subspace, and a skew-product in a general setting.     

New parameters of subsets in polynomial association schemes

We define new parameters, a zero interval and a dual zero interval, of subsets in P- or Q-polynomial association schemes. A zero interval of a subset in a P-polynomial association scheme is a successive interval index for which the inner distribution vanishes, and a dual zero interval of a subset in a Q-polynomial association scheme is a successive interval index for which the dual inner distribution vanishes. We derive bounds of the lengths of a zero interval and a dual zero interval using the degree and dual degree respectively, and show that a subset in a P-polynomial association scheme (resp. a Q-polynomial association scheme) having a large length of a zero interval (resp. a dual zero interval) induces a completely regular code (resp. a Q-polynomial association scheme). Moreover, we consider the spherical analogue of a dual zero interval.     

A recognition algorithm for the intersection graphs of directed paths in directed trees

Consider a finite family of non-empty sets. The intersection graph of this family is obtained by representing each set by a vertex, two vertices being connected by an edge if and only if the corresponding sets intersect. The intersection graph of a family of directed paths in a directed tree is called a directed path graph. In this paper we present an efficient algorithm which constructs to a given graph a representation by a family of directed paths on a directed tree, if one exists. Also, we prove that a graph is a proper directed path graph if and only if it is a directed path graph.