局部紧H半群上概率测度序列的组合收敛性

首先讨论可数离散H半群上组合收敛的概率测度序列的一些极限性质,证明了相关文献中关于组合收敛必要条件的一个猜想.其次当半群具有交换性时,在同分布场合建立了强Kloss准则,证明经适当的shift变换可使概率测度卷积幂序列收敛到某个不变测度.最后讨论具有紧核的局部紧H半群上的概率测度卷积序列聚点集的构造.这些结果推广和改进了一些已有的结论.     

拓扑半群上概率测度序列组合收敛性的若干极限定理

本文研究了拓扑半群上概率测度序列{μ_n}的组合收敛性,即卷积序列μ_(k,n):=μ_(k+1)*μ_(k+2)*…*μ_n的极限性质.通过对概率测度支撑集代数结构的研究,首先得到可数离散半群上概率测度序列组合收敛的一个充分条件,它推广了经典的Marksimov定理,也推广和改进了文献中已有的一些结果.其次给出了局部紧H半群上概率测度卷积序列{μ_(k,n):0≤kn}极限点集的一个构造定理,它是群上经典结果在这类半群上的推广.     

紧L-X半群上不同分布的组合乘积的极限性质

本文讨论一类紧拓扑半群上不同分布概率测度组合乘积的极限性质,利用“局部群化”的方法将紧群上,紧交换半群上的一些结果以相应的形式建立到紧L-X半群上.     

局部紧半群上概率测度的强一致组合收敛性

讨论局部紧拓扑半群上相互独立但不同分布的概率测度卷积序列的极限性质、首先研究测度子半群与其支撑集在结构上的相依性,进而通过支撑集的代数结构在局部紧拓扑半群上给出一个概率测度序列强一致组合收敛的充要条件,并在此基础上找出一类拓扑半群S,使得当μ_k,n(?)λ_k,能确保λ_k(?)某个Haar测度.     

一类紧半群上概率测度的强组合收敛性

本文讨论紧半群上概率测度的强组合收敛性，通过对概率测度支撑集代数结构的研究，得到了一些充分条件与必要条件，这些结果推广了文献[1]-[3]中的相应结论。     

拓扑半群上概率测度的条件组合收敛与SHIFT组合收敛

本文用部分群化的方法,研究拓扑半群上概率测度的条件组合收敛性与SHIFT组合收敛性,得到了一些充分条件,并推广了一些组合收敛性结果.     

局部紧拓扑半群上概率测度卷积幂的若干极限定理

我们通过研究极限测度的不变性质，讨论了局部紧拓扑半群上概率测度卷积幂的若干极限性状．推广了[1]－[3]中的若干结果．     

基于互动与反馈的概率语言多属性群决策模型

针对概率语言多属性群决策问题,提出了基于互动与反馈的概率语言多属性群决策模型。首先定义了概率语言的距离测度和概率语言矩阵的一致性测度,以决策者的总体一致性测度确定决策者的客观权重,结合决策者的主观权重以主客观组合赋权法确定决策者的最终权重;结合概率语言的距离测度改进灰色关联度法,以归一化的属性关联度确定属性权重;为达到群决策中决策者的最大共识度,建立了具有互动与反馈过程的决策模型;最后提出了基于互动与反馈的概率语言多属性群决策模型的决策步骤,并且通过算例分析证明了该模型的有效性与可行性。     

一类可数离散半群上概率测度序列的组合收敛性

本文讨论具有单位元的可数离散半群上概率测度序列的组合收敛性，主要结果推广了有限群上的Ｍａｋｓｉｍｏｖ定理，同时也蕴含了Ｃｅｎｔｅｒ，Ｍｕｋｈｅｒｊｅａ等人的一些结论．     

一类随机过程的最优序贯检验的唯一性

§1 引言与结果概述设(x_1,t≥0)是概率空间(Ω,(?),p_i)(i=1.2)上的右连续随机过程,这里P_1和p_2是两个概率测度。我们来考虑检验问题:P_1是否是真正的概率测度?零假设是H_1:P_1是真正的概率测度,对立假设是H_2:P_2是真正的概率测度。我们要来探讨这个检验问题的最优检     

Strong uniform convergence of composition sequences of probability measures on locally compact topological semigroups

Weak convergence of convolution products of non-identical probability measures on topological semigroups is investigated. Firstly, the dependence relationship between the semigroupN of measures and suppN is studied; secondly, a necessary and sufficient condition that insures the strong uniform composition convergence of sequence μ_n is presented; thirdly, a more extensive class of semigroups is found, on which μ_n must be of strong uniform composition convergence, if it is of composition convergence.     

Stable convergence of the log-likelihood ratio to a mixture of infinitely divisible distributions

Some results concerning the asymptotic behavior of the log-likelihood ratio (LLR) and also of certain other random variables closely associated with the likelihood ratio are presented. More specifically, in the present paper we formulate the conditions for the stable convergence in distribution of the LLR for two sequences of the probability measures to a mixture of infinitely divisible distributions with finite variance. Moreover, the notion of a locally asymptotically mixed infinitely divisible (LAMID) sequence of parametric families of the probability measures is introduced, and it is shown that when a certain kind of differentiability-type regularity condition is satisfied, the given sequence of families satisfies the LAMID condition. These results extend and supplement the previous investigations of the author concerning non-Gaussian asymptotic distributions in statistics. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part III.     

Convergence in probability of random power series and a related problem in linear topological spaces

A linear topological space is said to have the circle property if every power series with coefficients in it has a circle of convergence. Every complete locally convex or locally bounded space has the circle property, but not a certain class ofF-spaces including the space of all random variables on a non-atomic probability space, endowed with the topology of convergence in probability. Research sponsored by the National Science Foundation under Grant No. GP 6035.     

Uniform Convergence of Probability Measures: Topological Criteria

Uniform convergence of probability measures is analyzed by topologizing the space of events. A new characterization of narrow (weak) convergence of probability measures on Polish space is also obtained.     

局部紧H半群上概率测度卷积幂的弱收敛性

本文讨论局部紧Ｈ半概率测度卷积幂的弱收敛性,将紧群上的Ｋａｗａｄａ－Ｉｔｏ型结果以某种相应的形式建立到局部紧Ｈ半群,由于紧半群上的概率测度卷积幂序列必为 ,所以,不仅Ｋａｗａｄａ－Ｉｔｏ经典结果是本文的特例,而且「１」中的定理和「２」中的定理２都可以作为本文定理的推论     

The Poisson Boundary of Amenable Extensions

 We obtain two new criteria of amenability of a closed normal subgroup H in a locally compact group G. The first one is formulated in terms of convergence of convolutions of probability measures on G, and the second one in terms of the Poisson boundaries of random walks on G and on the quotient group G/H. Received 10 April 2001; in revised form 18 December 2001     

Asymptotic error distribution for the Euler scheme with locally Lipschitz coefficients

In traditional works on numerical schemes for solving stochastic differential equations (SDEs), the globally Lipschitz assumption is often assumed to ensure different types of convergence. In practice, this is often too strong a condition. Brownian motion driven SDEs used in applications sometimes have coefficients which are only Lipschitz on compact sets, but the paths of the SDE solutions can be arbitrarily large. In this paper, we prove convergence in probability and a weak convergence result under a less restrictive assumption, that is, locally Lipschitz and with no finite time explosion. We prove if a numerical scheme converges in probability uniformly on any compact time set (UCP) with a certain rate under a global Lipschitz condition, then the UCP with the same rate holds when a globally Lipschitz condition is replaced with a locally Lipschitz plus no finite explosion condition. For the Euler scheme, weak convergence of the error process is also established. The main contribution of this paper is the proof of $\sqrt{n}$ weak convergence of the normalized error process and the limit process is also provided. We further study the boundedness of the second moments of the weak limit process and its running supremum under both global Lipschitz and locally Lipschitz conditions.     

Approximation by Bézier variants of the BBHK operators

In this work a new type of approximation operator—the Bézier variant of the BBHK operator—is introduced. Its approximation properties are studied. A convergence theorem for such approximation operators for locally bounded functions is established by means of some techniques of probability theory and analysis methods. This convergence theorem subsumes the approximation of functions of bounded variation as a special case.