Conditional Empirical Processes Defined by Nonstationary Absolutely Regular Sequences

K. I. Yoshihara (1990,Comput. Math. Appl.19, No. 1, 149–158) proved the weak invariance of the conditional nearest neighbor regression function estimator called the conditional empirical process based on-mixing observations. In this paper, we extend the result for nonstationary and absolutely regular random variables which have applications for Markov processes, for which the initial measure is not necessary, the invariant measure.     

非线性奇摄动系统的渐近性态

The asymptotic behavior of solution for a n-dimensional nonlinear singularly perturbed system is studied. Under the appropriate assumptions, the existence of solution for the system is proved and the estimation of the solution is given using the method of differential inequalities.     

一类正则Sturm—Liouville问题特征的渐近分析

考虑[0,π]上一类带一般分离型边界条件的正则Sturm—Liouville问题特征的渐近表示,利用Frechet导数,对特征值进行精细的分析,清楚地给出了方程系数q（x）及边界条件中常数cot α,col β对特征值的影响．使结论更具一般化．     

Asymptotic Behavior of a Class of Perturbed Differential Equations

Ukrainian Mathematical Journal - We consider the problem of stability of nonlinear differential equations with perturbations. Sufficient conditions for global uniform asymptotic stability in terms...     

时间随机环境下随机游动的渐近行为

本文给出了可数状态空间中时间随机环境下随机游动的一个统一的模型 .对于最常见的情况 ,即d维最近邻域随机环境下随机游动 ,如果环境是严平稳的 ,则在一定条件下 ,该随机游动满足强大数定律和中心极限定理 .特别地 ,当环境独立同分布时 ,我们可以得到更为具体的结果 ,该结果类似于经典的随机游动的相应结论 .     

连续型随机变量序列的一类强偏差定理

设｛犡狀,狀≥１｝是任意相依连续型随机变量序列,｛犅狀,狀≥１｝是实直线上的Ｂｏｒｅｌ集,犐犅狀（狓）是犅狀的示性函数．该文研究｛犐犅狀（犡狀）,狀≥１｝的极限性质,得到一类用不等式表示的强偏差定理,其偏差界依赖于样本点．     

On the Asymptotic Behavior of Perturbed Strongly Continuous Semigroups

For a strongly continuous semigroup (T(t))_t≥0 with generator A on a Banach space X and an A–bounded perturbation B we characterize norm continuity and compactness of the terms in the Dyson–Phillips series of the perturbed semigroup (S(t))_t≥0 .This allows us to characterize uniform exponential stability of (S(t))_t≥0 by spectral conditions on (T(t))_t≥0 and A + B. The results are applied to a delay differential equation.     

On the Asymptotic Behavior of the Remainder of a Dirichlet Series Absolutely Convergent in a Half-Plane

For a Dirichlet series with nonnegative exponents and zero abscissa of absolute convergence, we study the asymptotic behavior of the remainder , < 0, as n .     

Asymptotic Behavior of Predator-Prey Systems Perturbed by White Noise

In this paper, we develop the results in Rudnicki (Stoch. Process. Appl. 108:93–107, 2003) to a stochastic predator-prey system where the random factor acts on the coefficients of environment. We show that there exists the density functions of the solutions and then, study the asymptotic behavior of these densities. It is proved that the densities either converges in L ¹ to an invariant density or converges weakly to a singular measure on the boundary.     

二阶半线性奇摄动边值问题解的渐近行为

该文研究非法向双曲条件下的二阶半线性奇摄动边值问题解的渐近行为.利用边界层函数法,构造了区间端点处的代数型边界层,获得了问题的一致有效渐近解;利用微分不等式理论,证明了解的存在性以及渐近解与精确解之间的误差估计.通过一个典型的算例,验证了该文的理论结果.     

一类非线性奇摄动Robin问题解的渐近性态

利用渐近理论和微分不等式的方法,该文研究了一类非线性奇摄动Robin问题. 证明了其解的存在性,并得到了解的任意n 阶一致有效渐近展开式.     

Asymptotic Behavior of the Solutions of Boundary-Value Problems for Singularly Perturbed Integrodifferential Equations

Ukrainian Mathematical Journal - We study the asymptotic behavior of the solutions of a boundary-value problem with boundary jumps for linear integrodifferential equations of the third order with...     

Asymptotic Behavior of Increments of Random Fields

We derive universal strong laws for increments of sums of i.i.d. random variables with multidimensional indices without an exponential moment. Our theorems yield the strong law of large numbers, the law of the iterated logarithm, and the Csorgo-Revesz laws for random fields. New results are obtained for distributions from domains of attraction of the normal law and of completely asymmetric stable laws with index (1, 2). Bibliography: 18 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 298, 2003, pp. 191–207.     

The Asymptotic Behavior of the Ruin Probability within a Random Horizon

Subject to the assumption that the common distribution of claim sizes belongs to the extendedregular variation class,the present work obtains a simple asymptotic formula for the ruin probability within arandom or nonrandom horizon in the renewal model.     

The Asymptotic Behavior of a Family of Sequences via Tauberian Theorems

We study the asymptotic behavior of a family of sequences defined by the following nonlinear induction relation c₀ = 1 and c_n ∑^k_{j = 1} r_jc_[n/mj] + ∑^k_{j = k + 1} r_jc_{[(n + 1)^1/mj] − 1} for n ≥ 1, where the r_j are real positive numbers and m_j are integers greater than or equal to 2. Depending on the fact that ∑^k_{j = 1} r_j is greater or lower than 1, we prove that c_n/n^α or c_n/(ln n)^α goes to some finite limit for some explicit α. Our study is based on Tauberian theorems and extends a result of Erdös et al.     

一类随机算子随机不动点的迭代序列收敛性

利用非对称迭代技巧,讨论了一类不具有紧性条件的随机算子的随机不动点的存在唯一性,并给出了迭代序列收敛于解的误差估计,所得结果是某些已知结果本质改进和推广.     

一类两参数半线性奇摄动问题解的渐近性态

本文研究了一类两参数半线性奇摄动问题的基本模型.利用奇摄动方法,对该问题解的结构在两个小参数相互关联的三种不同情形下作了讨论.得到了该问题在三种不同情形下的渐近解并证明了在三种情形下解的结构与渐近性态.     

删失数据的光滑乘积限估计的渐近性质

在删失数据的模型下，对于光滑未知的分布函数Ｆ０，文中提出了光滑化的方法去估计Ｆ０，得到了光滑ＰＬ估计Ｆｎ，并建立了Ｆｎ在Ｄ（－∞，Ｔ），Ｔ＜ＴＦ上的弱收敛和强相合的结果．同时也获得了光滑ＰＬ过程的强逼近和重对数律．     

带停留对称随机游动局部时的渐进行为

该文研究带停留对称随机游动,模型的局部时可写成一个非退化两物种分支过程的泛函.由这个表示建立模型局部时的收敛性质.