可加Lvy过程的轨道渐近性质

本文主要研究有限个相互独立的从属过程之和的样本轨道的渐近性质.给出了样本轨道在零点附近和无穷远处的渐近增长率的上下极限,并且得出了在零点附近渐近增长率的一致下极限.     

Krawtchouk多项式的渐近性态

在前人的基础上,对Krawtchouk多项式及其零点的渐近性态进行了研究.首先推导出对于任意固定的u=n/N∈(0,P)或(0,q)Krawtchouk多项式Kn(λN)(其中λ=xN,0<λ<1)的一致有效渐近展开式.然后又得到了它的零点的渐近性态,并对其相应的误差限进行分析.该误差限为o(n-4/3).     

Krawtchouk多项式零点的渐近展开及其误差限

Krawtchouk多项式在现代物理学中有着广泛应用．基于Li和Wong的结果,利用Airy函数改进了Krawtchouk多项式的渐近展开式,而且得到了一个一致有效的渐近展开式A·D2进一步,利用Airy函数零点的性质,推导出了Krawtchouk多项式零点的渐近展开式,并讨论了其相应的误差限．同时还给出了Krawtchouk多项式和其零点的渐近性态,它优于Li和Wong的结果．     

相协样本下Wilcoxon两样本统计量的渐近分布北大核心CSCD

研究了相协样本下Wilcoxon两样本统计量的渐近分布的问题.利用Hoeffding分解方法,获得了相协样本下Wilcoxon两样本统计量的渐近分布为正态分布的结果,推广了负相协样本下Wilcoxon两样本统计量的渐近分布的结果.     

奇异随机偏微分方程中参数MLE的渐近性质

对一类带有未知参数和小干扰项的奇异随机偏微分方程,基于连续样本轨道,给出了参数的极大似然估计,证明了当干扰项趋于0时,参数估计量的强相合性和渐近正态性.     

相协样本下Wilcoxon两样本统计量的渐近分布

研究了相协样本下Wilcoxon两样本统计量的渐近分布的问题.利用Hoeffding分解方法,获得了相协样本下Wilcoxon两样本统计量的渐近分布为正态分布的结果,推广了负相协样本下Wilcoxon两样本统计量的渐近分布的结果.     

一类整函数零点的渐近公式

借助Rouché定理、留数定理及渐近分析的方法,给出了整函数f(z)=zmsinz-α(0≠α∈R,m∈Z+)零点的渐近公式及渐近迹.这种方法也适用于其它整函数的零点估计.     

多组样本下GL－统计量的渐近性质

本文上要讨论多组样本下GL－统计量的渐近分布。这里我们使用了Gâteaut微分逼近方法,在多组i.i.d.样本下,给出了GL－统计量的渐近正态分布的一组条件,从而拓广了i.i.d.样本下GL－统计量的渐近正态分布的性质[1].     

多组样本下GL—统计量的渐近性质

本文主要讨论多组样本下GL－统计量的渐近分布,这里我们使用了Gateaut微分逼近方法,在多组i.i.d.样本下,给出了GL－统计量的渐近正态分布的一组条件,从而拓广了i.i.d样本下GL－统计量的渐近正态分布的性质[1]。     

强混合样本下最近邻密度估计的渐近正态性

研究了α-混合样本下最近邻密度估计的渐近性质,证明了估计的渐近正态性并且给出了其渐近方差的显式表达式,由此构造了α-混合样本下概率密度的渐近置信区间.     

Catalytic branching random walks in ℤ d with branching at the origin

A time-continuous branching random walk on the lattice ? ^d , d ≥ 1, is considered when the particles may produce offspring at the origin only. We assume that the underlying Markov random walk is homogeneous and symmetric, the process is initiated at moment t = 0 by a single particle located at the origin, and the average number of offspring produced at the origin is such that the corresponding branching random walk is critical. The asymptotic behavior of the survival probability of such a process at moment t → ∞ and the presence of at least one particle at the origin is studied. In addition, we obtain the asymptotic expansions for the expectation of the number of particles at the origin and prove Yaglom-type conditional limit theorems for the number of particles located at the origin and beyond at moment t.     

The Gaussian approximation for generalized Friedman’s urn model with heterogeneous and unbalanced updating

The Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.Its asymptotic properties have been studied by many researchers.In literature,it is usually assumed that the expected number of balls added at each stage is a constant in despite of what type of balls are selected,that is,the updating of the urn is assumed to be balanced.When it is not,the asymptotic property of the Friedman’s urn model is stated in the book of Hu and Rosenberger(2006) as one of open problems in the area of adaptive designs.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a general multi-color Friedman type urn model with heterogeneous and unbalanced updating.The Gaussian process is a solution of a stochastic differential equation.As an application,we obtain the asymptotic properties including the asymptotic normality and the exact law of the iterated logarithm.     

Asymptotic behavior of spectral of Neumann‐Poincaré operator in Helmholtz system

In this paper, we are concerned with the asymptotic behavior of the Neumann‐Poincaré operator in Helmholtz system. By analyzing the asymptotic behavior of spherical Bessel function near the origin and/or approach higher order, we prove the asymptotic behavior of spectral of Neumann‐Poincaré operator when frequency is small enough and/or the order is large enough. The results show that spectral of Neumann‐Poincaré operator is continuous at the origin and converges to 0 from the complex plane in general.     

Localization results for densities associated with stable small-noise diffusions

Summary This paper concerns asymptotic properties of the stationary density associated with small-noise diffusion processes, such as considered in the well-known work of Ventcel and Freidlin [12]. We assume that the origin is a globally attracting asymptotically stable equilibrium point of the underlying deterministic flow. For a bounded domain D, containing the origin, we derive estimates which establish the asymptotic independence, as the size of the noise vanishes, of the equilibrium density in D from the coefficients of the process outside D. These results are applied to generalize a result of Sheu [10] on an asymptotic representation of the equilibrium density.     

Properties of the Michaelis-Menten mechanism in phase space

We study the two-dimensional reduction of the Michaelis-Menten reaction of enzyme kinetics. First, we prove the existence and uniqueness of a slow manifold between the horizontal and vertical isoclines. Second, we determine the concavity of all solutions in the first quadrant. Third, we establish the asymptotic behaviour of all solutions near the origin, which generally is not given by a Taylor series. Finally, we determine the asymptotic behaviour of the slow manifold at infinity. To this end, we show that the slow manifold can be constructed as a centre manifold for a fixed point at infinity.     

Abelian and Tauberian results for the one-dimensional modified Stockwell transforms

The aim of this paper is to study the asymptotic behavior of one- dimensional modified Stockwell transform of a tempered distribution signal through the quasiasymptotic behavior at origin or infinity of the signal itself. More precisely, we give some Abelian results which mean that we derive the asymptotic properties of the S-transform of a tempered signal from the quasiasymptotic properties of the signal itself and we do also the opposite. So, we also give some Tauberian results which describe some quasiasymptotic properties of the tempered signal by means of the asymptotic properties of its Stockwell transform.     

Laws of the iterated logarithm for iterated Wiener processes

The recent interest in iterated Wiener processes was motivated by apparently quite unrelated studies in probability theory and mathematical statistics. Laws of the iterated logarithm (LIL) were independently obtained by Burdzy⁽²⁾ and Révész⁽¹⁷⁾. In this work, we present a functional version of LIL for a standard iterated Wiener process, in the spirit of functional asymptotic results of an ²-valued Gaussian process given by Deheuvels and Mason⁽⁹⁾ in view of Bahadur-Kiefer-type theorems. Chung's liminf sup LIL is established as well, thus providing further insight into the asymptotic behavior of iterated Wiener processes.     

Construction of an asymptotic expansion for the solution of a linear system of equations of neutral type with a small delay in the absence of a boundary layer

In this paper we simplify the algorithm for constructing the asymptotic expansion for the solution of a linear system of neutral type at a large distance from the origin. After using the Laplace transformation to determine the asymptotic expansion near the initial point, we succeed in reducing the problem of determining the initial conditions to the computation of the residues of certain functions for which we have recurrence formulas.Translated from Matematicheskie Zametki, Vol. 6, No. 1, pp. 109–113, July, 1969.