WEAK UNCORRELATEDNESS OF RANDOM VARIABLES

New measures of independence for n random vaxiables, based on their moments, are studied. A scale of degrees of independence for random variables which starts with uncorrelatedness (for n = 2) and finishes at independence is constructed. The scale provides a countable linearly ordered set of measures of independence.     

ON THE UNIFORM CONSISTENCY OF THEKAPLAN-MEIER ESTIMATOR UNDER HEAVY CENSORING

Let X,i.i.d. and Y1i. i.d. be two sequences of random variables with unknown distribution functions F(x) and G(y) respectively. X, are censored by Y1. In this paper we study the uniform consistency of the Kaplan-Meier estimator under the case ey=sup(t:F(t)＜1)＞to=sup(t2G(t)＜1) The sufficient condition is discussed.     

LOCAL MEDIAN ESTIMATION OF VARIANCE FUNCTION

This paper considers local median estimation in fixed design regression problems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong convergence rates of the proposed estimators are obtained. Simulation results are given to show the performance of the proposed methods.     

ON THE STRONG LAW OF LARGE NUMBERS

This paper introduces the concept of BC sequences and investigates some conditions which imply the strong law of large numbers for these sequences. The authors also study the strong law of large numbers for general random variable sequences. As applications of the result the authors characterize p-smoothableness of Banach space. Some generalizations of Petrov theorem, the Marcinkiewicz-Zygmund theorem and Hoffmann-Jorgensen and Pisier theorem are obtained.     

LARGE DEVIATION FOR THE EMPIRICAL CORRELATION COEFFICIENT OF TWO GAUSSIAN RANDOM VARIABLES

In this article,the author obtains the large deviation principles for the empir- ical correlation coefficient of two Gaussian random variables X and Y.Especially,when considering two independent Gaussian random variables X,Y with the means EX. EY (both known),wherein the author gives two kinds of different proofs and gets the same results.     

THE LAW OF ITERATED LOGARITHM FOR R／S STATISTICS

A law of iterated logarithm for R/S statistics with the help of the strong approximations of R/S statistics by functions of a Wiener process is shown.     

LARGE SAMPLE PROPERTIES OF THE SIR IN CDMA WITH MATCHED FILTER RECEIVERS

The output signal-to-interference (SIR) of conventional matched filter receiver in random environment is considered. When the number of users and the spreading factors tend to infinity with their ratio fixed, the convergence of SIR is showed to be with probability one under finite fourth moment of the spreading sequences. The asymptotic distribution of the SIR is also obtained.     

A BIVARIATE EXTENSION OF BLEIMANN－BUTZER－HAHN OPERATOR

Let C( R ^2) be a class of continuous functions f on R ^2.A bivariate extension Ln(f,x,y)of Bleiman-Butzer-Hahn operator is defined and its standard convergence properties are given.Moreover,a local analogue of Voronovskaja theorem is also give for a subclass of C(R ^2).     

相依随机变量和的极限理论

本文对各种混合r.w.序列及相伴r.w.序列的有关结果作一概略介绍。     

《概率论与数理统计》中有关独立性一反例的深入分析

独立性是《概率论与数理统计》是的一个非常重要的概念.教学中在说明随机变量函数独立性时会涉及许多反例.本文就有关随机变量函数独立性的一个反例作了进一步的推广分析.     

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

1.IntroductionandMainResultsAsequence{X.,n21}ofrealvaluedrandomvariablesissaidtosatisfythelawoflargenumbersofHsu-Robbins(1947)typewithasequence{b.}ofrealnumbersifVP(ISn-b.I2ne)< co,Ve>0,(1.1)ZP(ISn-b.I2ne)< co,Ve>0,(1.1)n=1whereS.~ZXi.Conditionsunderwhich(1.1)holdswerediscussedinmanypapers.Ai=1moregeneralresultforlidrealvaluedrandomvariablesisgivenin[2].LetBbearealseparableBanachspacewithnorm11'11and{X.}asequenceofB-valuedrandomelemefltsandputSa~ZXi,n21.Candcdenotepositivefinitecon…     

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.     

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     

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).     

The law of the iterated logarithm and Marcinkiewicz law of large numbers forB-valuedU-statistics

Suppose thatB is a separable Banach space and (S,l,P) a probability space.H is a measurable symmetric kernel function fromS ^m intoB. In this paper we shall further study some limit theorems forB-valuedU-statisticsU _m ⁿ H based onP andH. Special attention is paid upon the Marcinkiewicz type law of large numbers and the law of the iterated logarithm. Our results can be regarded as extensions of corresponding results for sums of independentB-valued random variables toU-statistics.Research supported by National Natural Science Foundation of China and Zhejiang Province.     

A Note on the Use of V and U Statistics in Nonparametric Models of Regression

We establish the asymptotic equivalence of V and U statistics when the statistic’s kernel depends on n. Combined with a lemma of B. Lee this result provides conditions under which U statistics projections and V statistics are asymptotically equivalent. The use of this equivalence in nonparametric regression models is illustrated with several examples; the estimation of conditional variances, skewness, kurtosis and the construction of a nonparametric R-squared measure.     

Recurrence of matrix cocycles

This paper considers measurable cocycles with values in the subgroup of SL(2, ℂ) of diagonal and skew-diagonal matrices over an ergodic transformation preserving the probability measure. We prove the recurrence of such cocycles under certain conditions as well as the equivalence of two definitions of the recurrence.     

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.     

Large deviations for Langevin spin glass dynamics

Summary We study the asymptotic behaviour of asymmetrical spin glass dynamics in a Sherrington-Kirkpatrick model as proposed by Sompolinsky-Zippelius. We prove that the annealed law of the empirical measure on path space of these dynamics satisfy a large deviation principle in the high temperature regime. We study the rate function of this large deviation principle and prove that it achieves its minimum value at a unique probability measureQ which is not markovian. We deduce that the quenched law of the empirical measure converges to _Q . Extending then the preceeding results to replicated dynamics, we investigate the quenched behavior of a single spin. We get quenched convergence toQ in the case of a symmetric initial law and even potential for the free spin.     

A new approach to the giant component problem

We study the largest component of a random (multi)graph on n vertices with a given degree sequence. We let n → ∞. Then, under some regularity conditions on the degree sequences, we give conditions on the asymptotic shape of the degree sequence that imply that with high probability all the components are small, and other conditions that imply that with high probability there is a giant component and the sizes of its vertex and edge sets satisfy a law of large numbers; under suitable assumptions these are the only two possibilities. In particular, we recover the results by Molloy and Reed on the size of the largest component in a random graph with a given degree sequence. We further obtain a new sharp result for the giant component just above the threshold, generalizing the case of G(n,p) with np = 1 + ω(n)n^?1/3, where ω(n) → ∞ arbitrarily slowly. Our method is based on the properties of empirical distributions of independent random variables, and leads to simple proofs. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009