同分布 ρ 混合序列的最大值不等式及其应用

设X_n,n≥1是同分布的ρ混合序列, 记S_n=∑ⁿ_{i=1 Xi}. 该文讨论了$\max\limits_{1\leq i\leq n}\frac{|S_i|}{i}$ $(n\geq1)$的分布函数的上界. 作为应用,获得了随机变量$\sup\limits_{n\geq1}\frac{|S_n|}{n}$的1阶矩及$p(>1)$阶矩分别存在有限的充分必要条件,这是一个与独立同分布场合相一致的结果.     

关于Ciesielski 的一个问题

1984年,在索菲亚举行的国际函数构造论会议上,Ciesielski,Z.问在规范化条件下,对二个n次多项式的卷积的上确界是否有“好”的估计?本文给以否定的回答.     

PERIODIC BOUNDARY VALUE PROBLEMS FOR DIFFERENTIAL EQUATIONS WITH “SUPREMUM”

In this paper, the monotone iterative method of Lakshmikantham and a comparison result are applied to study a periodic boundary value problem for a nonlinear impulsive differential equation with "supremum" and the existence of maximal and minimal solutions are obtained.     

On the Asymptotic Behavior of the Harmonic Renewal Measure

We study the tail behavior of the harmonic renewal measure U= _n=1 (1/n)F ^n* where F is a probability distribution with finite negative mean and F ⁿ * is the n-fold convolution of F. As an application of the obtained result on U, we give alternative proofs of some known results concerning the tail behavior of the supremum and the first positive sum of a random walk with negative drift.     

双侧加权广义逆的上确界和稳定性

本文利用矩阵A ∈C_r~(m×n)可表示为其所有r×r非奇异子矩阵的逆的凸线性组合,推导出双侧加权广义逆的上确界,并讨论这些上确界稳定的充分和必要条件.     

B值拟鞅不等式及其应用

本文给出B值拟鞅的概率不等式与集合不等式,并用它们刻划了B空间的p可光滑性及q可凸性,作为应用,还证明了B值拟鞅的强大数律,收敛速度及极大值函数的可积性。