二维泊松方程的高精度紧致差分方法

利用对称性和待定系数的基本思想，提出了数值求解泊松方程的一种新的高阶紧致差分方法。构造了二堆泊松方程的四阶和六阶紧致盖分格式。数值算倒验证了方法的精确性和可靠性。     

A ‘Striking’ Demonstration of the Poisson Distribution

This article describes a simple classroom activity that helps students immediately visualize and understand the meaning and mathematical properties of the Poisson distribution.     

A Probability Distribution With No Memory

This article considers and then illustrates an apparent pardox associated with the exponential distribution, which is known as the “Memoryless Property”.     

外汇汇率买入的带跳扩散股票的期权定价

通过建立股票价格服从带跳扩散过程的随机微分方程和外币汇率的随机微分方程,研究与之相关联的欧式期权定价问题,并通过鞅定价方法推导出买入欧式期权的定价公式。     

The Most Salient Matches in the History of Premier League Football

What are the most surprising, most impressive and most exciting matches in the history of the highest division of English football? Fans, clubs, critics and broadcasters often attempt to interpret and compare the outcomes of football matches. This can be useful as a means of building a reputation for and interest in a particular club, match or competition. However, such analysis is often subjective with fan bias, personal preference and the prize on offer influencing expectation and interpretation of the results. In this paper statistical measures are developed to identify the most surprising, most impressive and most exciting outcomes from an objective ex post point of view. To achieve this it is assumed that goal scoring in soccer can approximately be considered as a Poisson process. First, the most surprising outcomes are estimated as those with the lowest Poisson probability to occur. Second, the most impressive outcomes are identified by their so-called Skellam percentile position. This measure varies between 0 and 1 and has a close relationship with the p-value in statistical testing. Finally, the most exciting match is identified by measuring the variability in the win expectancy during a match.     

Converse Result on Szász-Type Operators

Szász-type operators can be constructed by a Poisson process. The purpose of this paper is to derive the converse result in connection with Szász-type operators by Steckin-Marchaud-type inequalities and new Ditzian modulus of continuity. The degree of approximation on deterministic signals is also given.     

不同再保费定价原则下的最优再保险

根据两种不同的再保费定价原则,即安全附加原则和方差原则,当索赔分布为指数分布时,分别讨论了使调整系数最大或破产概率最小的最优自留水平,为保险公司进行最优再保险提供决策依据.     

三维调和方程的狄利克雷问题的解法

对于问题1,一般采用分离变量法和Legendre多项式求解,而本人直接用球的泊松公式求解,通过坐标轴的旋转,巧妙地给出了夹角γ表达式.     

一类冲击模型的期望损伤

研究了冲击次数服从泊松过程、损坏是可加的冲击模型,给出了期望损坏,从而为评估系统寿命提供依据.     

复合广义泊松过程的可加性

广义泊松过程常常出现在顾客成批到达或成批服务的排队问题中。已有文献运用概率母函数的方法证明了广义齐次泊松过程的可加性。在此基础上,该文运用特征函数的方法证明了复合广义泊松过程也具有与广义齐次泊松过程相似的可加性。