巴氏空间中独立随机元部分和的完全收敛性

设｛Ｘｎ，ｎ≥１｝是Ｂａｎａｃｈ空间Ｂ中的独立非同分布的随机元序列，本文给出了｛Ｘｎ，ｎ≥１｝分别为对称和非对称两种条件下的Ｈｓｕ－Ｒｉｂｂｉｎｓ型强大数定律。     

随机环境中分枝随机游动的极限定理

假定环境平稳遍历, 考虑随机环境中的分枝随机游动. 在此模型中, 粒子以上临界的Galton-Watson 过程分枝产生后代, 而以一维紧邻随机环境中的随机游动进行运动. 令~$Z_{n}(B)$ 表示时间~$n$ 落于~$B$ 中的粒子数, 其中~$B$ 为~$\mathbb{R}$ 中任一子集. 得到了计数测度~$Z_{n}(\cdot)$ 经过适当的规范化之后, 在~``annealed" 情形下的中心极限定理.     

距离空间上的几乎处处中心极限定理

该文得到了关于一般可分距离空间上独立随机元序列的几乎处处中心极限定理(almost sure central limit theory, 简记为ASCLT). 作为应用, 该文给出了取值于可分Banach空间上随机元序列以及一类随机场序列满足ASCLT的充分条件,最后给出了关于多维随机变量序列极值的ASCLT.     

两指标鞅差序列的中心极限定理及其在平稳随机场上的应用

本文讨论了两指标鞅差序列及平稳随机场上的中心极限定理.所考虑的鞅差是根据平面格点的序:(s₁,s₂)<(t₁,t₂)当且仅当s_1...     

B值L^p极限鞅的若干性质

本文在1≤p<∞的情形下讨论了取值于 Banach 空间的 L~p 极限鞅的收敛性质,给出了 L~p 极限鞅的 Riesz 分解,并用 L~p 极限鞅的收敛性刻划了空间的 Radon-Nikodym 性质,从而把在 p=1情形下的一些结果推广到了1≤p<∞的情形。此外,还指出了 B 值 p 拟鞅,B 值 p 一致渐近鞅与本文中的 B 值 L~p 极限鞅之间的包含关系。     

非紧致一秩Riemann对称空间上的中心极限定理

我们在本文中研究非紧致一秩Ｒｉｅｍａｎｎ对称空间上初等球函数的渐近表示,并利用Ｌｏｈｏｕｅ Ｎ．和Ｒｙｃｈｎｅｒ Ｔｈ．得到的热核表达式,建立起这类空间上的非欧中心极限定理,所得结果包含了Ｔｅｒｒａｓ的定理作为其特例．     

非紧致一秩Rienann对称空间上的中心极限定理

我们在本文中研究非紧致一秩Riemann对称空间上初等球函数的渐近表示,并利用LohoueN.和RychnerTh.得到的热核表达式,建立起这类空间上的非欧中心极限定理,所得结果包含了Terras的定理作为其特例.     

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.     

Estimation of Mean and Covariance Operator of Autoregressive Processes in Banach Spaces

The autoregressive model in a Banach space (ARB) contains many continuous time processes used in practice, for example, processes that satisfy linear stochastic differential equations of order k, a very particular case being the Ornstein–Uhlenbeck process. In this paper we study empirical estimators for ARB processes. In particular we show that, under some regularity conditions, the empirical mean is asymptotically optimal with respect to a.s. convergence and convergence of order 2. Limit in distribution and the law of the iterated logarithm are also presented. Concerning the empirical covariance operator we note that, if (X _n, n ∈ &Zopf;) is ARB then (X _n ⊗ X _n, n ∈ &Zopf;) is AR in a suitable space of linear operators. This fact allows us to interpret the empirical covariance operator as a sample mean of an AR and to derive similar results for it. This revised version was published online in August 2006 with corrections to the Cover Date.     

B值随机元的Rosenthal不等式及其应用

该文证明了一类B值随机元序列的Rosenthal不等式,一些经典的Rosenthal不等式作为其推论被蕴含其中.作为不等式的应用,还给出了行为鞅差随机元的阵列的完全收敛性的一些结果,推广和改进了一些熟知的结论.     

The Law of the Iterated Logarithm and Central Limit Theorem for L-Statistics

The Chung–Smirnov law of the iterated logarithm and the Finkelstein functional law of the iterated logarithm for empirical processes are used to establish new results on the central limit theorem, the law of the iterated logarithm, and the strong law of large numbers for L-statistics with certain bounded and smooth weight functions. These results are used to obtain necessary and sufficient conditions for almost sure convergence and for convergence in distribution of some well-known L-statistics and U-statistics, including Gini's mean difference statistic. A law of the logarithm for weighted sums of order statistics is also presented.     

Critical Behavior in Almost Sure Central Limit Theory

Let X ₁,X ₂,… be i.i.d. random variables with EX ₁=0, EX ₁²=1 and let S _k =X ₁+⋅⋅⋅+X _k . We study the a.s. convergence of the weighted averages

On the Number of Subgraphs of a Specified Form Embedded in a Random Graph

Let U ₁, U ₂,... be a sequence of i.i.d. random elements in R^d. For x>0, a graph G _n (x) may be formed by connecting with an edge each pair of points in that are separated by a distance no greater than x. The points of G _n (x) could represent the stations in a telecommunications network and the edge set the lines of communication that exist among them. Let be a collection of graphs on mn points having a specified form or structure, and let denote the number of subgraphs embedded in G _n (x) and contained in . It is shown that a SLLN, CLT and LIL for follow easily from the theory of U-statistics. In addition, a uniform (in x) SLLN is proved for collections that satisfy a certain monotonicity condition. Some applications are mentioned and the results of some simulations presented. The scaling constants appearing in the CLT are usually hard to obtain. These are worked out for some special cases.     

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。     

Functional Limit Theorems for Multiparameter Fractional Brownian Motion

We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional Lévy’s modulus of continuity and many other results are its particular cases. Applications to approximation theory are discussed.      

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.     

Weak Laws with Random Indices for Arrays of Random Elements in Rademacher Type p Banach Spaces

For a sequence of constants {a _n,n1}, an array of rowwise independent and stochastically dominated random elements { V _nj, j1, n1} in a real separable Rademacher type p (1p2) Banach space, and a sequence of positive integer-valued random variables {T _n, n1}, a general weak law of large numbers of the form is established where {c _nj, j1, n1}, _n , b _n are suitable sequences. Some related results are also presented. No assumption is made concerning the existence of expected values or absolute moments of the {V _nj, j1, n1}. Illustrative examples include one wherein the strong law of large numbers fails.     

A nonclassical LIL for geometrically weighted series in Banach space

Let {X, Xn ; n ≥ 0} be a sequence of independent and identically distributed random variables, taking values in a separable Banach space (B,||·||) with topological dual B* . Considering the geometrically weighted series ξ(β) =∑∞n=0βnXn for 0 β 1, and a sequence of positive constants {h(n), n ≥ 1}, which is monotonically approaching infinity and not asymptotically equivalent to log log n, a limit result for(1-β2)1/2||ξ(β)||/(2h(1/(1-β2)))1/2 is achieved.