Functional Central Limit Theorems for Supercritical Superprocesses

In this paper, we establish some functional central limit theorems for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. In the particular case when the state \(E\) is a finite set and the underlying motion is an irreducible Markov chain on \(E\), our results are superprocess analogs of the functional central limit theorems of Janson (Stoch. Process. Appl. 110:177–245, 2004) for supercritical multitype branching processes. The results of this paper are refinements of the central limit theorems in Ren et al. (Stoch. Process. Appl. 125:428–457, 2015).     

D-W超过程的两个极限定理

该文讨论了Ｄ-Ｗ 超过程的累积半群的一些性质，并证明了Ｄ-Ｗ 超过程的两个条件极限定理，将Ｌｉ［６］中的结果推广到超过程的情形     

Central Limit Theorems for Supercritical Superprocesses with Immigration

In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with immigration with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem extends and generalizes the results obtained by Ren et al. (Stoch Process Appl 125:428–457, 2015). We first give laws of large numbers for supercritical superprocesses with immigration since there are few convergence results on immigration superprocesses, then based on these results, we establish the central limit theorem.     

关于超过程的几个比较定理

本文讨论了超Dawson-Watanabe过程的Laplace变换之间的相互比较,得到了依赖于其底过程和分枝特征的若干比较定理.应用比较定理可以将超布朗运动在特殊分枝下的某些性质推广到一般的超过程.同时将这些结果应用于非线性发展方程,得到了一类非线性发展方程的解之间的比较.     

一类暂留稳定过程的极限定理

本文研究了Ａ型暂留稳定过程在无穷远处的收敛速度，给出了一个重对数律．同时我们也得出了这类过程在起始点附近的一些性质．这些性质推广了［１］中的结果     

一类超一致椭圆扩散过程的极限定理

本文研究了分支特征为ψ（x,z）=γz^1+β（0<β≤1）形式的超一致椭圆扩散过程,当初始值X₀（dx）为底过程的某类不变测度时,给出了当空间维数d满足βd≤2时,超过程X_t依分布收敛于0测度,当βd>2时,X_t则依分布收敛于一个非退化的随机测度.     

Central and Functional Central Limit Theorems for a Class of Urn Models

We consider an approach based on tails to certain central limit and functional central limit theorems for a class of two color urn models. In particular, some of the results are derived from an associated Ornstein–Uhlenbeck process, and for another result we give an alternative proof based on martingale tails.      

一类适应随机变量序列的强极限定理

研究了一类适应随机变量序列的局部收敛性,推广了文献[1]中的结论.并在假定部分和序列为极限鞅时,得到了极限鞅的强极限定理.最后给出了*-mixing序列的强大数定律.     

Spatial Central Limit Theorem for Supercritical Superprocesses

We consider a measure-valued diffusion (i.e., a superprocess). It is determined by a couple \((L,\psi )\), where L is the infinitesimal generator of a strongly recurrent diffusion in \(\mathbb {R}^{d}\) and \(\psi \) is a branching mechanism assumed to be supercritical. Such processes are known, see for example, (Englander and Winter in Ann Inst Henri Poincaré 42(2):171–185, 2006), to fulfill a law of large numbers for the spatial distribution of the mass. In this paper, we prove the corresponding central limit theorem. The limit and the CLT normalization fall into three qualitatively different classes arising from “competition” of the local growth induced by branching and global smoothing due to the strong recurrence of L. We also prove that the spatial fluctuations are asymptotically independent of the fluctuations of the total mass of the process.     

极限相对对数似然比与一类强偏差定理

本文引进极限相对对数似然比γ（ω）的概念,并利用它来研究相依离散随机变量序列的极限性质。得到了一类用不等式表示的强极限定理,本文称之为强偏差定理,其偏差界依赖于γ（ω）。     

临界Galton-Watson过程条件极限定理的构造性证明

对临界Galton-Watson 过程,本文通过精细地构造条件Galton-Watson 树的方法, 在第n代不灭绝的条件下研究第nt代粒子数Z_nt的构造性性质(0nt^l和Z_nt^r.本文分别给出了{Z_nt^l/n│Z_n>0 }和{Z_nt^r/n│Z_n>0} 的条件极限性质,用概率的方法部分地解释了Spitzer, Lamperti和Ney的经典条件极限的结果. 最后还给出了最近共同祖先的条件分布.     

关于可列非齐次马尔可夫链的一类强极限定理

本文的目的是要给出关于可列非齐次马尔可夫链M元状态序组出现频率的一类新形式的强极限定理，所得结论对任意可列非齐次马尔可夫链普遍成立。     

A Class of Strong Limit Theorems and Moment Generating Function Method

In virtue of the notion of likelihood ratio and moment generating function,the limit properties of the sequences of absolutely continuous random variables are studied,and a class of strong limit theorems represented by inequalities with random bounds are obtained.     

一类强极限定理和矩母函数方法

In virtue of the notion of likelihood ratio and moment generating function,the limit properties of the sequences of absolutely continuous random variables are studied,and a class of strong limit theorems represented by inequalities with random bounds are obtained.     

非齐次树上m阶非齐次马氏连的一类强极限定理

树指标随机过程已成为近年来发展起来的概率论的研究方向之一.强极限定理一直是国际概率论界研究的中心课题之一.通过构造适当的非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,研究给出了一类非齐次树上m阶非齐次马氏链的若干强极限定理.     

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.     

广义Bethe树上关于随机选择系统的一类极限定理

本文将随机选择系统的概念在广义 Bethe 树上进行了推广,同时研究了广义Bethe树上选择子序列的状态序偶出现频率的一类极限定理,它是 Bernoulli序列无规则性概念的进一步推广.     

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.     

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.