基于子样分位数和刀切法的统计推断

本文考虑对母体分位数之函数作统计推断的问题.子样分位数之函数的渐近分布为正态.使用刀切法,我们给出了渐近分布的方差与协方差的估计量并建立了它们的一致性.这些结果提供了一些在渐近意义下正确的统计推断方法.     

除数和函数对平方补数的均值

对于任意正整数n的平方补数c（n）,研究了其除数和函数σ（c（n））均值的渐近性,并利用解析方法得到了一个渐近公式。     

带灾难和移民的n维分枝过程

本文考虑了带灾难和移民的n维分枝过程有效灾难的首次发生时间.首先讨论了Q-矩阵生成函数的性质,通过生成函数给出了有效灾难首次发生时间概率密度函数的Laplace变换的表达式,数学期望,方差.并得到了该模型有效灾难首次发生时间的期望的渐近性质.     

带灾难和拯救的n维分枝过程

本文考虑了带灾难和拯救的n维分枝模型有效灾难的首次发生时间.首先讨论了Q矩阵生成函数的性质,通过生成函数给出了有效灾难首次发生时间概率密度函数的Laplace变换的表达式、数学期望和方差,并得到了该模型有效灾难首次发生时间的期望的渐近性质.     

带有灾难和依赖状态控制的成批到达成批服务排队模型

本文考虑一类带灾难的成批到达和成批服务的依赖状态的控制排队模型有效灾难的首次发生时间.首先讨论q-矩阵发生函数的性质,通过发生函数给出有效灾难首次发生时间概率密度函数的Laplace变换的精确表达式、数学期望和方差,并得到了该模型有效灾难首次发生时间的期望的渐近性质.     

数列的渐近展开和极限

把数列通项看作是母函数的幂级数展开系数,由母函数所满足的微分方程,得到了数列的递推关系式.把母函数展开为基本函数(1-x)~(-α)的线性叠加,由基本函数幂级数展开系数的渐近展开,得到了数列的渐近展开和一些极限值.     

与Hermite多项式和广义Laguerre多项式相关联的双正交多项式系统

生成函数刻画了正交多项式的很多重要性质.本文的主要目的是根据生成函数的特点研究正交多项式类之间的渐近关系.本文拓展了Lee及其合作者的工作,构造一类双正交多项式系统,并由此构造出分别渐近于Hermite多项式和广义Laguerre多项的函数列;给出渐近于Hermite多项式和广义Laguerre多项的函数列的判定定理.作为这些性质的应用,可以直接获得若干正交多项式和组合多项式的渐近表示,从而验证了揭示超几何多项式渐近关系的Askey格式成立.     

两项指数和及两项特征和的混合均值

利用解析方法以及高斯和的性质研究一类二项指数和及二项特征和的混合均值问题,并给出一个精确的表示式.作为应用,给出该和式的一个渐近公式以及该和式与Dirichlet L-函数加权均值的一个较强的渐近公式.     

N-种群Lotka-Volterra扩散竞争反馈控制生态系统的持久性和全局渐近性

本文研究了一类具有ai类功能性反应函数的n种群非自治Lotka-Volterra扩散竞争反馈控制生态系统的持久性和全局渐近性．利用比较原理和构造Lyapunov函数分别得到系统的持久生存与全局渐近稳定的充分条件．     

奇异值、拟共形映射和Schottky上界

获得了Ramanujan模方程奇异值的若干性质 (包括渐近精确的界 ) ,并由此得出了Hersch Pflugerφ-偏差函数和Agardη-偏差函数的无穷乘积表示 ,改进了显式拟共形Schwarz引理 ,获得了Schottky上界新型的渐近精确的估计 ,证实了关于线性偏差函数的一个猜测     

二维递归序列的渐近性

In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values.     

Asymptotics on Two-dimensional Recursion Sequences

In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values.     

Asymptotic formulas related to the $$M_2$$M2-rank of partitions without repeated odd parts

The Ramanujan Journal - We give asymptotic expansions for the moments of the $$M_2$$-rank generating function and for the $$M_2$$-rank generating function at roots of unity. For this we apply the...     

Euler数，Bernoulli数及有序Bell数的渐近估计

利用特殊函数的发生函数为亚纯函数的特点,给出Euler数、Bernoulli数、有序Bell数等几个组合数的带有余项的渐进估计．     

On Estimating the Cumulant Generating Function of Linear Processes

We compare two estimates of the cumulant generating function of a stationary linear process. The first estimate is based on the empirical moment generating function. The second estimate uses the linear representation of the process and the empirical moment generating function of the innovations. Asymptotic expressions for the mean square errors are derived under short- and long-range dependence. For long-memory processes, the estimate based on the linear representation turns out to have a better rate of convergence. Thus, exploiting the linear structure of the process leads to an infinite gain in asymptotic efficiency.     

Analytic combinatorics of chord and hyperchord diagrams with k crossings

Using methods from Analytic Combinatorics, we study the families of perfect matchings, partitions, chord diagrams, and hyperchord diagrams on a disk with a prescribed number of crossings. For each family, we express the generating function of the configurations with exactly k crossings as a rational function of the generating function of crossing-free configurations. Using these expressions, we study the singular behavior of these generating functions and derive asymptotic results on the counting sequences of the configurations with precisely k crossings. Limiting distributions and random generators are also studied.     

Words with a generalized restricted growth property

Words where each new letter (natural number) can never be too large, compared to the ones that were seen already, are enumerated. The letters follow the geometric distribution. Also, the maximal letter in such words is studied. The asymptotic answers involve small periodic oscillations. The methods include a chain of techniques: exponential generating function, Poisson generating function, Mellin transform, depoissonization.     

Distributions of the Numbers of Failures and Successes in a Waiting Time Problem

Abstract. In this article we consider infinite sequences of Bernoulli trials and study the exact and asymptotic distribution of the number of failures and the number of successes observed before the r-th appearance of a pair of successes separated by a pre-specified number of failures. Several formulae are provided for the probability mass function, probability generating function and moments of the distribution along with some asymptotic results and a Poisson limit theorem. A number of interesting applications in various areas of applied science are also discussed.     

Weight of a link in a shortest path tree and the Dedekind Eta function

The weight of a randomly chosen link in the shortest path tree on the complete graph with exponential i.i.d. link weights is studied. The corresponding exact probability generating function and the asymptotic law are derived. As a remarkable coincidence, this asymptotic law is precisely the same as the distribution of the cost of one “job” in the random assignment problem. We also show that the asymptotic (scaled) maximum interattachment time to that shortest path tree, which is a uniform recursive tree, equals the square of the Dedekind Eta function, a central function in modular forms, elliptic functions, and the theory of partitions. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

The q-Catalan Numbers: A Saddle Point Approach

Using the saddle point method, we obtain from the generating function of the q-Catalan numbers and Cauchy’s integral formula asymptotic results in central and non-central regions.