A Note on the Almost Sure Central Limit Theorem for Partial Sums of ρ^(−)-Mixing Sequences

Let be a strictly stationary sequence of ρ?-mixing random variables. We proved the almost sure central limit theorem, containing the general weight sequences, for the partial sums , where , . The result generalizes and improves the previous results.

Complete Convergence Properties of the Sums for -mixing Sequences of Random Variables

This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.

Strong Law of Large Numbers and Complete Convergence for Sequences of -Mixing Random Variables

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.

Complete Convergence and Weak Law of Large Numbers for <i><span style="text-decoration:overline;">ρ</span></i>-Mixing Sequences of Random Variables

In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the classical weak law of large numbers, etc. from independent sequences of random variables to ρ-mixing sequences of random variables without necessarily adding any extra conditions.

Complete Convergence for Weighted Sums of φ-mixing Sequence

In this paper, the complete convergence and strong law of large numbers for weighted sums of φ-mixing sequence with different distribution are investigated under some weaker moment conditions. Our results extend ones of independent sequence with identical distribution to the case of φ-mixing sequence with different distribution.

STUDY ON THE SEQUENCE STRUCTURE OF BUTADIENE-STYRENE RUBBER BY ^(13)C-NMR METHOD V.CALCULATION METHOD OF DIAD COMPOSITION

The calculating equations which could be used to obtain diad composition from the peakintensities of carbon spectra were derived. The result of the microstructure calculated from thediad compositions was in good agreement with that obtained through IR or;H-NMR measurement.

STUDY ON THE SEQUENCE STRUCTURE OF SBR BY ^(13)C—NMR METHOD Ⅰ. ASSIGNMENT FOR UNSATURAT CARBONS SPECTRA

The sequence structures of emulsion-processed SBR and solution-processed (by lithium catalyst) SBR were investigated by ^(13)C-NMR spectroscopy. Seventeen peaks within unsaturated carbon region were recorded under the adopted experimental conditions. Assignments for these peaks were made by empirical-parameter-evaluation method.

LARGE DEVIATIONS FOR SOME DEPENDENT SEQUENCES

Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny （Stochastic Process. Appl. 96 （2001） 143） obtained the estimation μ（Sn 〉 n） ≤ cn^-p/2, Yulin Li （Statist. Probab. Lett. 62 （2003） 317） generalized the result to the case when p ∈ （1,2] and obtained μ（Sn 〉 n） ≤ cn^l-p, these are optimal in a certain sense. In this article, the authors study the large deviation of Sn for some dependent sequences and obtain the same order optimal upper bounds for μ（Sn 〉 n） as those for martingale difference sequence.

Convergence Rate of Estimator forNonparametric Regression Model under ρ-mixing Errors

In this paper, we investigate the nonparametric regression model based on ρ-mixing errors, which are stochastically dominated by a nonnegative random variable. Weobtain the convergence rate for the weighted estimator of unknown function g（x） in pth-mean, which yields the convergence rate in probability. Moreover, an example of the nearestneighbor estimator is also illustrated and the convergence rates of estimator are presented.

SUBSTITUENT CHEMICAL SHIFT (SCS) AND THE SEQUENCE STRUCTURE OF ETHYLENE-VINYL ALCOHOL COPOLYMERS

Three ethylene-vinyl alcohol copolymers were studied by means of the substituent chemical shift (SCS) method. The SCS parameters of hydroxy (-OH) in two different solvents were obtained: in deuterium oxide/phenol (20/80 W/W ) the parameters are S_1 = 42.77±0.08ppm, S_2 = 7.15±0.06 ppm, S_3 (s)= -4.08±0.02ppm, S_3 (t) =-3.09±0.20ppm,S_4 = 0.48±0.03ppm, S_5 = 0.26±0.05ppm. In o-dichloro-benzen-d_4 S_1(s)=44.79±0.61ppm, S_2=7.40±0.00ppm, S_3(s)=-4.51±0.17ppm, S_3(t)=-3.13 ±0.00 ppm, S_4 =0.63±0.04ppm, S_5=0.36±0.00ppm.Simultaneously the ^(13)CNMR spectra of EVA copolymers were assigned by using the SCS parameters obtained.

A LOW OF THE ITERATED LOGARITHM FOR DOUBLE ARRAY SUM OF φp-MIXING SEQUENCE

I. INTRODUCTION AND SOME LEMMASLet{εi} be independent random variables, E（εi） = 0, E（εi2） =σ2, sup E[εi|r【∞ for some r】2, {ani} be a double array of constants satisfying proper conditions. Ref. [1] gave

Rates of uniform convergence for empirical processes of strictly stationary β-mixing sequences indexed by an unbounded class of functions

Assume that {Xn} is a strictly stationary β-mixing random sequence with the β-mixing coefficient βk = O(k-r), 0 < r ≤1. Yu (1994) obtained convergence rates of empirical processes of strictly stationary β-mixing random sequence indexed by bounded classes of functions. Here, a new truncation method is proposed and used to study the convergence for empirical processes of strictly stationary β-mixing sequences indexed by an unbounded class of functions. The research results show that if the envelope of the index class of functions is in Lp, p > 2 or p > 4, uniform convergence rates of empirical processes of strictly stationary β-mixing random sequence over the index classes can reach O((nr/(l+r)/logn)-1/2) or O((nr/(1+r)/ log n)-3/4) and that the Central Limit Theorem does not always hold for the empirical processes.

Complete convergence of ρ-mixing sequence

Let {Xn, n≥1} be a sequence of random variables and let Sn=∑1≤i≤nXi,n-=σ（Xi1≤i≤n）,n+=σ（Xi,i≥n）,n≥1.

^(13)C-NMR STUDY OF ETHYLENE-1-OCTENE COPOLYMERS

A ^(13)C-NMR method is presented for a quantitative determination of the respective monomercomposition and sequence distributions in ethylene-1-octene copolymers prepared with supportedtitanium/magnesium catalyst. On the basis of the sequence distributions, the ethylene-1-octenecopolymerization mechanism was studied. It was found that the observed sequence distributions inethylene-1-octene copolymers are satisfactorily predicted by the two-site model M/M,in whichthe copolymerization proceeds according to first-order Markovian statistics at the two differentsites.

矩条件下任意随机序列的一些收敛结果(英文)

Let {X n , n ≥ 1} be an arbitrary sequence of random variables. Some convergence results for the partial sums of arbitrary sequence of random variables are obtained, which generalize the known results for independent sequences, NA sequences, ρ-mixing sequences and φ-mixing sequences, and so on.

Strong Convergence of Partitioning Estimation for Nonparametric Regression Function under Dependence Samples

In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; partitioning estimation; strong convergence;φ-mixing sequences.

Strong Stability of Linear Forms in φ-Mixing Random Variables

In this paper some new results of strong stability of linear forms in φ-mixing random variables are given. It is mainly proved that for a sequence of φ-mixing random variables {xn,n≥1} and two sequences of positive numbers {an,n≥1} and {bn,n≥1} there exist d dn∈R,n = 1,2,..., such that bn^-1∑i=1^naixi-dn→0 a.s.under some suitable conditions. The results extend and improve the corresponding theorems for independent identically distributed random variables.

Laws of the Iterated Logarithm for-mixing Random Variables with Normal Distribution

Consider a ρ-mixing sequence of identically distributed random variables with the underlying dis- tribution in the domain of attraction of the normal distribution. This paper proves that law of the iterated logarithm holds for ρ-mixing sequences of random variables. Our results generalize and improve Theorems 1.2-1.3 of Qi and Cheng （1996） from the i.i.d, case to ρ-mixing sequences.

Unified Asymptotic Results for Maximum Spacing and Generalized Spacing Methods for Continuous Models

Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MSP method has been shown to be very useful for estimating parameters for univariate continuous models with a shift at the origin which are often encountered in loss models of actuarial science and extreme models. The MSP estimators have also been shown to be as efficient as maximum likelihood estimators in general and can be used as an alternative method when ML method might have numerical difficulties for some parametric models. Asymptotic properties are presented in a unified way. Robustness results for estimation and parameter testing results which facilitate the applications of the GSP methods are also included and related to quasi-likelihood results.

On the Hàjek-Rènyi Inequality

In this paper we give an elementary and unified proof of the Hajek-Renyi inequality, and get a general version of this inequality which not only covers the all known results but also derives some new results.