随机环境中分枝随机游动的极限定理

在随机环境中分枝随机游动模型中,粒子的繁衍机制是随机环境中分枝过程,各代粒子在直线上的位置由依赖随机环境的点过程给定,讨论了各代点过程的Laplace变换由其条件期望规范化后的极限性质.     

随机环境中受控分枝过程的极限定理

讨论了随机环境中受控分枝过程{Z_n:n∈N}的极限问题.给出了过程在{S_n:n∈N}下的规范化过程{W_n:n∈N}几乎处处收敛、L~1收敛和L~2收敛的充分条件,以及过程{W:n∈N}的极限非退化于0的充分条件和必要条件,得到了过程在{I_n:n∈N}下的规范化过程{W_n:n∈N}几乎处处收敛和L~1收敛的充分条件.     

NA序列中心极限定理的收敛速度

本文对NA（NegativelyAssociated）序列建立了中心极限定理的一致收敛速度，只要其三阶矩有限及描述NA序列协方差结构的一个系数u（n）被负指数序列所控制，而无需平稳性便获得了其收敛速度O（n(-1/2)logn）。     

随机二次型的极限定理及其应用

考虑形如s₁^T(S₁S₁^T)^ms₁, s₁^T(SS^T)^ms₁的二次型,在一个弱的矩条件下,获得了其强收敛、收敛速度等结果,并且给出了其在CDMA中的应用和模拟结果.     

Slutsky定理在样本分位数的极限分布证明上的应用

为了更好地理解和应用样本分位数的极限分布,利用Slutsky定理,推导了样本分位数的极限分布.     

多维随机向量序列加权和的中心极限定理

本文研究了多维随机向量序列加权和的渐近行为.利用Lindeberg中心极限定理的基本思想,得到了多维随机向量序列加权和的中心极限定理及其收敛速度,为Lindeberg中心极限定理的推广.     

独立随机序列最大值的几乎处处极限定理

本文研究了独立随机序列最大值分布的几乎必然收敛性.利用有关协方差的不等式和加权平均,获得独立随机序列最大值的几乎处处极限.将独立同分布随机序列的结论,推广了独立但不同分布的情形.     

带移民粒子系统的波动极限定理

证明了一类带移民粒子系统的波动极限,其极限过程是广义 Omstein-Uhlenbeck 过程,推广了已有文献的相应结果.     

带移民Jirina过程的弱极限定理

该文在矩条件下讨论了一列带移民Jirina过程的弱极限定理.按照极限过程的不同对矩条件作了简单分类.文章证明了在不同的矩条件下,一列带移民Jirina过程适当规范后可以在Skorokhod空间分别弱收敛到连续分支过程,带移民的连续分支过程,不连续的带移民分支过程以及确定性过程.对最后这种情形,还给出了一个波动极限定理.     

Limit Theorems for Stochastic Variational Inequalities with Non-Lipschitz Coefficients

Potential Analysis - We establish various limit theorems for one-dimensional stochastic variational inequalities with Yamada-Watanabe type conditions on the coefficients, including, the...     

关于任意随机变量序列的强极限定理的一个注记

主要说明两两NQD随机变量序列的一些收敛性质是任意随机变量序列的强极限定理的推论.     

Limit Theorems for Multiplicative Processes

Let W be a non-negative random variable with EW=1, and let {W _i } be a family of independent copies of W, indexed by all the finite sequences i=i ₁i _n of positive integers. For fixed r and n the random multiplicative measure ⁿ _r has, on each r-adic interval at nth level, the density with respect to the Lebesgue measure on [0,1]. If EW log Wr, the sequence { ⁿ _r } _n converges a.s. weakly to the Mandelbrot measure _r . For each fixed 1n, we study asymptotic properties for the sequence of random measures { ⁿ _r } _r as r. We prove uniform laws of large numbers, functional central limit theorems, a functional law of iterated logarithm, and large deviation principles. The function-indexed processes is a natural extension to a tree-indexed process at nth level of the usual smoothed partial-sum process corresponding to n=1. The results extend the classical ones for { ¹ _r } _r , and the recent ones for the masses of { _r } _r established in Ref. 23.     

Limit Theorems for General Markov Chains

Siberian Mathematical Journal -     

Limit Theorems for Non-Commutative Random Variables

We study the weak law of large numbers and the central limit theorem for non-commutative random variables. We first define the concepts of variance and expectation for probability measures on homogeneous spaces, and formulate the weak law of large numbers and the central limit theorem for probability measures on locally compact groups. Then, we consider the non-commutative case, where the homogeneous space is replaced by a C^*-algebra that is equipped with a locally compact group G of automorphisms. We define the concepts of variance and expectation in the non-commutative situation. Furthermore, we prove that the weak law of large numbers and the central limit theorem hold for non-commutative random variables on if they hold on the group G of automorphisms.     

Mixing Limit Theorems for Ergodic Transformations

We show that distributional and weak functional limit theorems for ergodic processes often hold for arbitrary absolutely continuous initial distributions. This principle is illustrated in the setup of ergodic sums, renewal-theoretic variables, and hitting times for ergodic measure preserving transformations.     

On Limit Theorems for Continued Fractions

It is shown that for sums of functionals of digits in continued fraction expansions the Kolmogorov-Feller weak laws of large numbers and the Khinchine-Lévy-Feller-Raikov characterization of the domain of attraction of the normal law hold.      

Approximate Central Limit Theorems

We refine the classical Lindeberg–Feller central limit theorem by obtaining asymptotic bounds on the Kolmogorov distance, the Wasserstein distance, and the parameterized Prokhorov distances in terms of a Lindeberg index. We thus obtain more general approximate central limit theorems, which roughly state that the row-wise sums of a triangular array are approximately asymptotically normal if the array approximately satisfies Lindeberg’s condition. This allows us to continue to provide information in nonstandard settings in which the classical central limit theorem fails to hold. Stein’s method plays a key role in the development of this theory.     

The Discounted Limit Theorems

The large deviation theorems, exponential inequalities and a non-uniform estimate of the Berry–Esséen theorem in a discounted version are proved.Dedicated to Professor Vytautas Statulevičius on the occasion of his 75th birthday.