复合泊松过程的可加性

对复合泊松分布可加性的研究在许多的文献中都可以看到,本文首先应用特征函数的方法证明了复合泊松分布的可加性.以此为基础,结合对随机过程相关性质的讨论,证明了复合泊松过程也具有与复合泊松分布可加性相似的,某种意义上的可加性性质.     

截尾平稳泊松过程及泊松流的分布

本文分析了区间〔０，＋∞〕上强度为λ（常数）的泊松过程的性质，提出了另一类新的模型－－截尾平稳泊松过程，得出了截尾平稳泊松过程的性质及泊松流的分布。     

泊松着色代数

首先,给出了泊松着色代数的定义及构造泊松着色代数的一种方法,其次,证明了在张量积的运算下泊松着色代数是封闭的,最后,通过容许泊松着色代数及其上的非结合二元运算等价定义了泊松着色代数.     

复合泊松过程及其在保险风险中的若干应用

本文利用齐次泊松过程的可加性,研究了复合泊松过程的可加性及其性质。作为应用,讨论了单个理赔额服从指数分布的复合泊松风险模型在第n次索赔时发生负盈余的概率。     

具有部分缺失数据的多个泊松总体的检验

本文给出了在两个泊松总体都以相同概率缺失时,检验两个总体的分布是否一致的似然比统计量,并给出了参数的估计值及其渐近正态性;进一步将这种方法推广到多个泊松总体的检验问题。     

泊松过程与时间变换

本文通过讨论时间齐次泊松过程和时间非齐次泊松过程之间的联系,指出在时间变换意义下,二者事实上是等价的.借此希望帮助本科学生加深对泊松过程的理解,启发学生对深一层次问题的思考.     

群胚上的Dirac结构及泊松约化

本文详细讨论了李双代数胚中的Dirac结构、群胚上的Dirac结构。利用Dirac结构的特征对的概念,给出了作用不变Dirac结构,拉回Dirac结构等概念的新的刻画。最后利用Dirac结构的有关性质,讨论了泊松齐性空间和泊松群胚作用的约化。     

G匚W上的泊松群胚结构

从泊松作用的角度考察了群胚上的半直积结构,定义了泊松群胚对泊松群胚的泊松作用,讨论了其性质,并证明了两个泊松群胚的半直积仍是泊松群胚,从而对群胚的半直积结构有了更多的认识.     

关于混合泊松分布之Willmot递推式的一个拓广

混合泊松分布的计算复杂与否视其结构分布而定.文章给出了结构分布密度函数满足一类一阶线性微分方程的混合泊松分布计算的递推式,它是Willmot递推式的一个拓广.     

基于高斯-泊松-莱斯利模型的中国人口预测与控制

针对中国人口现状和未来的发展趋势,提出了高斯-泊松-莱斯利模型,该方法全面考虑了人口年龄结构、人口性别比等因素,同时对成熟的莱斯利模型进行了优化改进.以此得到的分析结果可以为国家在人口问题方面的政策规划提出建设性的意见.     

Poisson on the poisson distribution

A translation of the totality of Poisson's own 1837 discussion of the Poisson distribution is presented, and its relation to earlier work of De Moivre is briefly noted.     

Poisson过程分解问题的一个注记

在研究Poisson过程分解问题时,现有文献的证明往往令人费解,本文主要运用极限理论,给出了一个简明易懂的证明.     

Poisson deleting derivations algorithm and Poisson spectrum

Cauchon [5 Cauchon, G. (2003). Effacement des dérivations et spectres premiers des algèbres quantiques. J. Algebra 260(2):476–518.[Crossref], [Web of Science ®] , [Google Scholar]] introduced the so-called deleting derivations algorithm. This algorithm was first used in noncommutative algebra to prove catenarity in generic quantum matrices, and then to show that torus-invariant primes in these algebras are generated by quantum minors. Since then this algorithm has been used in various contexts. In particular, the matrix version makes a bridge between torus-invariant primes in generic quantum matrices, torus orbits of symplectic leaves in matrix Poisson varieties and totally non-negative cells in totally non-negative matrix varieties [12 Goodearl, K. R., Launois, S., Lenagan, T. (2011). Torus invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves. Math. Z. 269(1):29–45.[Crossref], [Web of Science ®] , [Google Scholar]]. This led to recent progress in the study of totally non-negative matrices such as new recognition tests [18 Launois, S., Lenagan, T. (2014). E?cient recognition of totally non-negative matrix cells. Found. Comput. Math. 14:371–387.[Crossref], [Web of Science ®] , [Google Scholar]]. The aim of this article is to develop a Poisson version of the deleting derivations algorithm to study the Poisson spectra of the members of a class 𝒫 of polynomial Poisson algebras. It has recently been shown that the Poisson Dixmier–Moeglin equivalence does not hold for all polynomial Poisson algebras [2 Bell, J., Launois, S., Sanchez, O. L., Moosa, R. Poisson algebras via model theory and differential-algebraic geometry. J. Eur. Math. Soc. (to appear). [Google Scholar]]. Our algorithm allows us to prove this equivalence for a significant class of Poisson algebras, when the base field is of characteristic zero. Finally, using our deleting derivations algorithm, we compare topologically spectra of quantum matrices with Poisson spectra of matrix Poisson varieties.     

Poisson Distribution in the Polynomial Semigroup

We consider the asymptotic behavior of the distributions of arithmetic functions in polynomial semigroups.__________Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 429–442, October–December, 2004.     

Poisson Morphisms and Reduced Affine Poisson Group Actions

We establish the concept of a quotient affine Poisson group, and study the reduced Poisson action of the quotient of an affine Poisson group G on the quotient of an affine Poisson-G-variety V. The Poisson morphisms (including equivariant cases) between Poisson affine varieties are also discussed. Received April 5, 1999, Accepted March 5, 2001     

Population uncertainty and Poisson games

A general class of models is developed for analyzing games with population uncertainty. Within this general class, a special class of Poisson games is defined. It is shown that Poisson games are uniquely characterized by properties of independent actions and environmental equivalence. The general definition of equilibrium for games with population uncertainty is formulated, and it is shown that the equilibria of Poisson games are invariant under payoff-irrelevant type splitting. An example of a large voting game is discussed, to illustrate the advantages of using a Poisson game model for large games. Received December 1995/Revised version July 1997     

Poisson分布易被忽视的重要性质

"Poisson分布的总体均数与其观察单位成正比",这是一个被忽视的性质,但这是一个很基本的性质,在一些问题的解决中它是必需的.本文讨论了这个性质,并举例说明它在实际问题中的应用,然后对此内容在授课过程中的安排提出建议.