随机变量的截尾与任意随机变量序列的强极限定理

利用随机变量的截尾研究任意随机变量序列的性质,建立了一类矩条件下任意随机变量序列的强极限定理.作为推论,得到了可列非齐次马尔可夫过程的一个强极限定理,推广了鞅差序列当1≤p≤2和p≥2时的Chow定理,相应的一些已有结果和若干经典的关于独立随机变量序列的强大数定律是本文的特例。     

m-LNQD序列部分和的若干极限定理

作者提出了m-LNQD (m-linearly negative quadrant dependent)相依结构概念.首先给出了m-LNQD序列部分和的一个概率不等式,进而获得了m-LNQD序列的若干极限定理,推广了已有的结果.     

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.     

Central Limit Theorems for Exchangeable Random Variables When Limits Are Scale Mixtures of Normals

Central limit theorems for exchangeable random variables are studied when limits are scale mixtures of normals. First, necessary and sufficient conditions are given under the asymptotic tail probability condition for the mixands:

Limit Theorems for Stopped Functionals of Markov Renewal Processes

Some results for stopped random walks are extended to the Markov renewal setup where the random walk is driven by a Harris recurrent Markov chain. Some interesting applications are given; for example, a generalization of the alternating renewal process.     

可交换随机变量序列的随机极限定理

本文讨论了可交换随机变量序列{X_n:n≥1}的极限定理,得到了可交换随机变量序列的随机强大数律及加权和定理,并推广了文[4]中的结果.     

Central Limit Theorems for Random Permanents with Correlation Structure

Central limit theorems for permanents of random m×n matrices of iid columns with a common intercomponent correlation as n–m are derived. The results are obtained by introducing a Hoeffding-like orthogonal decomposition of a random permanent and deriving the variance formulae for a permanent with the homogeneous correlation structure.     

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.     

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.      

Limit Theorems for Sums of Heavy-tailed Variables with Random Dependent Weights

Let be independent and identically distributed random variables with heavy-tailed distributions. Consider a sequence of random weights , independent of and focus on the weighted sums , where μ involves a suitable centering. We establish sufficient conditions for these weighted sums to converge to non-trivial limit processes, as n→∞, when appropriately normalized. The convergence holds, for example, if is strictly stationary, dependent, and W ₁ has lighter tails than U ₁. In particular, the weights W _j s can be strongly dependent. The limit processes are scale mixtures of stable Lévy motions. We establish weak convergence in the Skorohod J ₁-topology. We also consider multivariate weights and show that they converge weakly in the strong Skorohod M ₁-topology. The M ₁-topology, while weaker than the J ₁-topology, is strong enough for the supremum and infimum functionals to be continuous. This research was partially supported by a fellowship of the Horace H. Rackham School of Graduate Studies at the University of Michigan and the NSF Grants BCS-0318209 and DMS-0505747 at Boston University.     

半直线上随机环境中随机游动的极限性质

文对右半直线上在0点带有反射壁的随机环境中随机游动进行了研究,得到了在环境是平稳遍历条件下的常返准则及在环境是独立同分布条件下的一个强大数定律和中心极限定理.     

随机变量序列函数的几乎处处中心极限定理

该文证明了随机元序列的一个一般的几乎处处中心极限定理, 并把这一结论应用于随机变量序列的函数.     

A new look at KK-theory

We describe the Kasparov group KK(A, B) as the set of homotopy classes of homomorphisms from an algebra qA associated with A into K B. The algebra qA consists of K-theory differential forms over A. Its construction is dual to that of M ₂(A). The analysis of qA and of its interplay with M ₂(A) gives the basic results of KK-theory.Partially supported by NSF.     

The smallness problem for -algebras

Akemann showed that any von Neumann algebra with a weak^* separable dual space has a faithful normal representation on a separable Hilbert space. He posed the question: If a C^*-algebra has a weak^* separable state space, must it have a faithful representation on a separable Hilbert space? Wright solved this question negatively and showed that a unital C^*-algebra has the weak^* separable state space if and only if it has a unital completely positive map, into a type I factor on a separable Hilbert space, whose restriction to the self-adjoint part induces an order isomorphism. He called such a C^*-algebra almost separably representable. We say that a unital C^*-algebra is small if it has a unital complete isometry into a type I factor on a separable Hilbert space. In this paper we show that a unital C^*-algebra is small if and only if the state spaces of all n by n matrix algebras over the C^*-algebra are weak^*-separable. It is natural to ask whether almost separably representable algebras are small or not. We settle this question positively for simple C^*-algebras but the general question remains open.     

关于NA随机变量极限定理的注记

NA随机变量是一包含独立随机变量在内的有广泛应用的随机变量类,本文在一些更弱的条件下,建立了具有不同分布NA随机变量列的强大数律和有界重对数律,进而推广了已有的关于NA随机变量的结果。     

Limit theorems for stationary random evolutions

On a separable Banach space, let A(ξ₁),A(ξ₂),... be a strictly stationary sequence of infinitesimal operators, centered so that EA(ξ_i) = 0, i = 1,2,.... This paper characterizes the limit of the random evolutions

as the solution to a martingale problem. This work is a direct extension of previous work on i.i.d. random evolutions.     

一类马尔可夫骨架过程的强大数定律和中心极限定理

基于马尔可夫骨架过程极限分布的已有研究结果,本文运用波莱尔-康特立引理、更新理论、科尔莫哥洛夫的强大数定律以及独立同分布情形的中心极限定理等重要理论,分别给出了一类马尔可夫骨架过程对应的累积过程满足强大数定律和中心极限定理的充分条件.     

Strong Approximation Theorems for Sums of Random Variables when Extreme Terms are Excluded

Let {X _n ;n≥1} be a sequence of i.i.d. random variables and let X ^(r) _n = X _j if |X _j | is the r-th maximum of |X ₁|, ..., |X _n |. Let S _n = X ₁+⋯+X _n and ^(r) S _n = S _n −(X ⁽¹⁾ _n +⋯+X ^(r) _n ). Sufficient and necessary conditions for ^(r) S _n approximating to sums of independent normal random variables are obtained. Via approximation results, the convergence rates of the strong law of large numbers for ^(r) S _n are studied. Received March 22, 1999, Revised November 6, 2000, Accepted March 16, 2001     

Classification of extensions of classifiable -algebras

For a certain class of extensions of C^*-algebras in which B and A belong to classifiable classes of C^*-algebras, we show that the functor which sends to its associated six term exact sequence in K-theory and the positive cones of K₀(B) and K₀(A) is a classification functor. We give two independent applications addressing the classification of a class of C^*-algebras arising from substitutional shift spaces on one hand and of graph algebras on the other. The former application leads to the answer of a question of Carlsen and the first named author concerning the completeness of stabilized Matsumoto algebras as an invariant of flow equivalence. The latter leads to the first classification result for nonsimple graph C^*-algebras.     

Asymptotic behaviors for percolation clusters with uncorrelated weights

We consider random processes occurring on bond percolation clusters and represented as a generalization of the “divide and color model” introduced by Häggström in 2001. We investigate the asymptotic behaviors for bond percolation clusters with uncorrelated weights. For subcritical and supercritical phases, we prove the law of large numbers and central limit theorems in the models corresponding to the so-called quenched and annealed probabilities.