Inequalities of Maximum of Partial Sums and Weak Convergence for a Class of Weak Dependent Random Variables

In this paper, we establish a Rosenthal-type inequality of the maximum of partial sums for ρ^- -mixing random fields. As its applications we get the Hájeck -Rènyi inequality and weak convergence of sums of ρ^- -mixing sequence. These results extend related results for NA sequence and p^＊ -mixing random fields,     

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.     

Some Convergence Sequences under Results for Arbitrary Moment Condition

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.     

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.``     

φ混合序列加权和的完全收敛性（英文）

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.     

$\rho^*$-混合随机变量列加权和的完全收敛性

In this paper, the complete convergence of weighted sums for ρ*-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete convergence of weighted sums for ρ*-mixing sequence of random variables are established. We not only promote and improve the results of Li et al. (J. Theoret. Probab., 1995, 8(1): 49-76) from i.i.d. to ρ*-mixing setting but also obtain their necessities and relax their conditions.     

Convergence Properties for Arrays of Rowwise φ-Mixing Random Variables

Convergence properties for arrays of rowwise(φ-mixing random variables are studied.As an application,the Chung-type strong law of large numbers for arrays of rowwiseφ-mixing random variables is obtained.Our results extend the corresponding ones for independent random variables to the case of φ-mixing random variables.     

Change-point Estimation of a Mean Shift in Moving-average Processes Under Dependence Assumptions

In this paper we discuss the least-square estimator of the unknown change point in a mean shift for moving-average processes of ALNQD sequence. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained. The results are also true for ρ-mixing, φ-mixing, α-mixing sequences under suitable conditions. These results extend those of Bai, who studied the mean shift point of a linear process of i.i.d, variables, and the condition ∑j=0^∞j｜aj｜ 〈 ∞ in Bai is weakened to ∑j=0^∞｜aj｜〈∞.     

A weak invariance principle for self-normalized products of sums of mixing sequences

Let variables in the {X, Xn, n ≥ 1} be a sequence of strictly stationary φ-mixing positive random domain of attraction of the normal law. Under some suitable conditions the principle for self-normalized products of partial sums is obtained.     

$\varphi$ 混合随机变量阵列的完全收敛性

Convergence properties for arrays of rowwise φ-mixing random variables are studied. As an application, the Chung-type strong law of large numbers for arrays of rowwise φ-mixing random variables is obtained. Our results extend the corresponding ones for independent random variables to the case of φ-mixing random variables.     

Strong Consistency for the Kernal Estimates of the Random Window Width of the Density Function and its Derivatives Under Φ—Mixing Samples

In the paper,we study the strong uniform consistency for the kernal estimates of random window width of density function and its derivatives under the condition that the sequence｛Xa｝of the sample are the identically Φ-mixing random variables.     

Moderate Deviations for M-estimators in Linear Models with φ-mixing Errors

In this paper, the moderate deviations for the M-estimators of regression parameter in a linear model are obtained when the errors form a strictly stationary φ-mixing sequence. The results are applied to study many different types of M-estimators such as Huber's estimator, Lp-regression estimator, least squares estimator and least absolute deviation estimator.     

ψ-混合序列的若干收敛结果(英文)

In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent random variable sequences without any extra conditions.     

The Strong Law of Large Numbers for ■-Mixing Random Variables

In this paper we present some results for the general strong laws of large numbers of ■-mixing random variables by a maximal inequality of Utev and Peligrad.These results extend and improve the related known works in the literature.     

The Strong Law of Large Numbers for ~(ρ)-Mixing Random Variables

In this paper we present some results for the general strong laws of large numbers of ~(ρ)-mixing random variables by a maximal inequality of Utev and Peligrad.These results extend and improve the rela...     

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.     

On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables

We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions. Consequently, we get the results for many dependent structures, such as END, ρ~*-mixing, ρ~--mixing and φ-mixing, etc.     

\rho混合随机变量的强大数律

In this paper we present some results for the general strong laws of large numbers of ■-mixing random variables by a maximal inequality of Utev and Peligrad.These results extend and improve the related known works in the literature.     

EXPONENTIAL INEQUALITIES FOR DEPENDENT RANDOM VARIABLES

This paper contains the Kolmogorov-Prokhorov exponential inequalities for dependent randomvariables, i.e., for φ-mixing, ρ--mixing and α--mixing. As an application, the law of iteratedlogarithm is established for stationary α--mixing sequence under a nearly best assumption.     

Complete moment convergence for sequence of identically distributed φ-mixing random variables

In the paper we extend and generalize some results of complete moment convergence results （or the refinement of complete convergence） obtained by Chow [On the rate of moment complete convergence of sample sums and extremes. Bull. Inst. Math. Academia Sinica, 16, 177-201 （1988）] and Li ＆ Spataru [Refinement of convergence rates for tail probabilities. J. Theor. Probab., 18, 933-947 （2005）] to sequences of identically distributed φ-mixing random variables.