EQUIVALENCE OF COMPLETE CONVERGENCE AND LAW OF LARGE NUMBERS FOR B-VALUED RANDOM ELEMENTS＇

Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number forB- valued independent random elements. The results of [10] become a simple corollary of the results here. At the same time, the author uses them to investigate the equivalence of strong and weak law of large numbers, and there exists an example to show that the conditions on probability are weaker. Project supported by the National Natural Science Foundation of China.     

NA随机变量序列的Egorov型强大数律的等价条件

本文研究了NA随机变量的Egorov型强大数律.利用NA随机变量的概率不等式,得到了NA随机变量序列的Egorov型强大数律的一些等价条件,所获结果推广和改进了在独立随机变量序列的Egorov的结果和在NA随机变量序列已有的一些结果.     

Asymptotics for dependent Bernoulli random variables

This paper considers a sequence of Bernoulli random variables which are dependent in a way that the success probability of a trial conditional on the previous trials depends on the total number of successes achieved prior to the trial. The paper investigates almost sure behaviors for the sequence and proves the strong law of large numbers under weak conditions. For linear probability functions, the paper also obtains the strong law of large numbers, the central limit theorems and the law of the iterated logarithm, extending the results by James et al. (2008).     

马氏环境中马氏链的一个概率不等式及其应用

本文研究了马氏环境中马氏链构成的随机变量之和的概率不等式问题.利用了结尾的方法,获得了马氏环境中马氏链构成的随机变量之和的尾部概率不等式,作为结果的应用,给出了将过程限制在(S,S∩F,PS)上的强大数定律.文中提出的方法和结果对研究独立的随机变量之和的大样本性质是十分有用的.     

Equivalent Conditions of Complete Convergence and Complete Moment Convergence for END Random Variables

In this paper, the complete convergence and the complete moment convergence for extended negatively dependent (END, in short) random variables without identical distribution are investigated. Under some suitable conditions, the equivalence between the moment of random variables and the complete convergence is established. In addition, the equivalence between the moment of random variables and the complete moment convergence is also proved. As applications, the Marcinkiewicz-Zygmund-type strong law of large numbers and the Baum-Katz-type result for END random variables are established. The results obtained in this paper extend the corresponding ones for independent random variables and some dependent random variables.     

重尾索赔下的一类相依风险模型的若干问题

本文研究了重尾索赔下的一类相依风险模型,得到了破产概率的尾等价式及索赔盈余过程大偏差的渐近关系式.在该模型中,一索赔到达过程是Poisson过程,另一索赔到达过程为其p-稀疏过程.     

Nash equilibrium and the law of large numbers

Pascoa (1993a) showed that the failure of the law of large numbers for a continuum of independent randomizations implies that Schmeidler's (1973) concept of a measure-valued profile function in equilibrium might not coincide with the concept of mixed strategies equilibrium of a nonatomic game. The latter should be defined as a probability measure on pure strategies profiles which is induced by the product measure of players' mixed strategies. This paper addresses existence and approximate purification of the latter and presents an assumption on continuity of payoffs that guarantees the equivalence between the two equilibrium concepts.     

非平稳NA随机变量满足迭对数律及大数定律的充分条件

本文应用Shao所提供的极大值矩不等式及概率不等式,给出了不具有平稳分布的NA随机变量列满足迭对数律和大数定律的充分条件.     

离散时间大种群随机多智能体系统的线性二次分散动态博弈

研究具有耦合二次型随机性能指标的离散时间大种群随机多智能体系统的分散博弈问题.系统所受的噪声干扰为条件二阶矩有界的鞅差序列,比以往研究所考虑的高斯白噪声情形更具有广泛性.采用状态聚集方法构造了对种群状态平均的估计,基于Nash必然等价原理设计了分散控制律,并利用概率极限理论分析了闭环系统的稳定性和最优性.主要结果包括(1)证明了对种群状态的平均的估计在某种范数意义下的强一致性,即种群状态的平均与其估计值之间的误差在该范数意义下将随系统个体数N的增加几乎必然收敛于0;(2)证明了闭环系统的几乎必然一致稳定性,即系统的稳定性与种群个体数N无关;(3)证明了所设计的分散控制律是几乎必然渐近Nash均衡策略.     

负相协D族广义Sparre-Andevsen模型下的大偏差及其应用

本文将经典的Sparre-Andevsen风险模型推广到保费收入过程不再是线性过程的一般风险过程,得到了一些关于负相协D族随机变量随机和的大偏差结果,以及破产概率的弱等价性.     

A mixed random walk on nonnegative matrices: A law of large numbers

In this paper a mixed random walk on nonnegative matrices has been studied. Under reasonable conditions, existence of a unique invariant probability measure and a law of large numbers have been established for such walks.     

STRONG LAW OF LARGE NUMBERS AND SHANNON-MCMILLAN THEOREM FOR MARKOV CHAINS FIELD ON CAYLEY TREE

1 lntroductionA tr(t(t is a grapl1 G = {T, E) wllicl1 is co1l11ected a11d colltai1ls no cir(.uits. Give11 a11y twov(irtic'is 't / P E T, let crP bc tl1e ullique patl1 col111ecti11g,v aIld /]. Defille tl1e graph distal1cc(l(rr, p) to hc the Ilu1llber of edges co11tained in the path crP.We discuss ulainly tl1e rooted Cayley tree TC,2(i.e.,binary tree. See Fig.1). In tlle Cayleytree Tc,2,tl1e root (denoted by 0) llas OIlly two 11(tiglll)(irs al1d all otller vertices have threeneighbors. A…     

Dual representation of convex sets of probability measures on totally bounded spaces

Convex sets of probability measures, frequently encountered in probability theory and statistics, can be transparently analyzed by means of dual representations in a function space. This paper introduces totally bounded spaces, whose structure is defined by a set of bounded real-valued functions, as a general framework for studying such representations. The reinterpretation of classical theorems in this framework clarifies the role of compactness and leads to simple existence criteria. Applications include results on the existence of probability measures satisfying given sets of conditions and an equivalence of consistent preferences and families of probability measures. Moreover, countable additivity of probabilities is seen to be a consequence of elementary consistency assumptions.     

凸数列的一个等价条件及其应用,Ⅱ

将涉及控制向量的凸数列的一个等价条件扩展到弱控制的情形，并给出此等价条件在代数、分析、凸体几何、概率论等诸多方面的应用。     

Uniform θ-equivalence of probability distributions based on information and related measures of discrepancy

Summary Some criteria based on K-L information number andW-divergence are presented for a certain type of uniform approximate equivalence of two probability distributions. As applications, some necessary and sufficient conditions are also given for the corresponding uniform asymptotic equivalence of two random sequences. The Institute of Statistical Mathematics     

NA随机变量列的有界重对数律

通过建立NA随机变量最大部分和的一些概率指数不等式，给出了具有不同分布的NA随机变量列有界重对数律的一些结果，因此推广了由R．Wittmann建立的独立随机变量的相关结果。     

Analysis of a Signorini problem with friction

This paper deals with the study of a nonlinear problem of frictionalcontact between an elastic body and a rigid foundation. Theelastic constitutive law is assumed to be nonlinear and thecontact is modelled with Signorini's conditions and a versionof Coulomb's law of dry friction. We present two weak formulationsof the problem and establish existence and uniqueness results,using arguments of elliptic variational inequalities and a fixed-pintproperty. Moreover, we prove some equivalence results and studythe behaviour of the solution when the coefficient of frictiontends to zero.     

Necessary conditions for the convergence of kullback-leibler’s mean information

Summary Two types of necessary conditions are given for the convergence of Kullback-Leibler’s mean information, one of which is connected with an asymptotic equivalence of two sequences of probability measures, and in special cases, with convergence of a sequence of probability distributions. The other is given in terms of the generalized probability density functions.     

Large deviations and the rate of convergence in the Birkhoff ergodic theorem

For bounded averaged functions, we prove the equivalence of the power-law and exponential rates of convergence in the Birkhoff individual ergodic theorem with the same asymptotics of the probability of large deviations in this theorem.     

Equivalence of laws and null controllability for SPDEs driven by a fractional Brownian motion

We obtain necessary and sufficient conditions for equivalence of law for linear stochastic evolution equations driven by a general Gaussian noise by identifying the suitable space of controls for the corresponding deterministic control problem. This result is applied to semilinear (reaction-diffusion) equations driven by a fractional Brownian motion. We establish the equivalence of continuous dependence of laws of solutions to semilinear equations on the initial datum in the topology of pointwise convergence of measures and null controllability for the corresponding deterministic control problem.