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.

Some Convergence Results for Sequences of -mixing Random Variables

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.

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.

Inequalities of Maximum of Partial Sums and Convergence Rates in the Strong Laws for ρ^-mixing Random Variables

在这份报纸，我们建立部分和的 Rosenthal 类型不平等为 -- 混合随机的变量。作为它的应用，我们在强壮的法律得到完全的集中率为 -- 混合随机的变量。获得的结果扩大相应结果。

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.

Moments of the maximum of normed partial sums of ρ^--mixing random variables

Let {Xn,n ≥ 1} be a sequence of identically distributed ρ^--mixing random variables and set Sn =∑i^n=1 Xi,n ≥ 1,the suffcient and necessary conditions for the existence of moments of supn≥1 ｜Sn/n^1/r｜^p（0 〈 r 〈 2,p 〉 0） are given,which are the same as that in the independent case.

Complete Convergence for Arrays of Rowwise Ч-mixing Random Variables

In the paper, the complete convergence for arrays of rowwise φ-mixing random variables is studied. Some sufficient conditions for complete convergence for an array of rowwise φ-mixing random variables without assumptions of identical distribution and stochastic domination are presented.

Complete moment convergence for ND random variables under the sub-linear expectations

In this article,we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND)random variables under the sub-linear expectations.As applications,we can obtain a series of results on complete moment convergence for ND random variables under the sub-linear expectations.

SOME LIMIT THEOREMS FOR SEQUENCES OF PAIRWISE NQD RANDOM VARIABLES

In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.

LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR m-NEGATIVELY ASSOCIATED RANDOM VARIABLES

M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.

ON CHOVER'S LIL FOR THE WEIGHTED SUMS OF STABLE RANDOM VARIABLES

Let {Xn,n ≥ 1} be a sequence of α-stable random variables(0 < α < 2), {ani,1 ≤ i≤ n, n≥1} be an array of constant real numbers. Under some restriction of {ani,1 ≤ i ≤ n,n≥1}, the authors discuss the integral test for the weighted partial sums {Σi=1naniXi,n ≥ 1}, and obtain the Chover's laws of iterated logarithm(LIL) as corollaries.

CONVERGENCE RATES IN THE STRONG LAWS OF NONSTATIONARYρ~*-MIXING RANDOM FIELDS

By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.

ON THE LIMITING BEHAVIOR OF THE MAXIMUM PARTIAL SUMS FOR ARRAYS OF ROWWISE NA RANDOM VARIABLES

Let {Xni, 1 ≤ n,i 〈 ∞} be an an array of rowwise NA random variables and {an, n ≥ 1} a sequence of constants with 0 〈 an ↑∞ . The limiting behavior of maximum partial sums 1/an max 1≤k≤n｜^k∑i=1 Xni｜ is investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [1] and Hu and Chang [2].

PRECISE ASYMPTOTICS IN SELF-NORMALIZED SUMS OF ITERATED LOGARITHM FOR MULTIDIMENSIONALLY INDEXED RANDOM VARIABLES

In the case of Z＋^d（d ≥ 2）-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z＋^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑n1/｜n｜（log｜n｜dP（｜Sn/Vn｜≥ε√log log｜n｜） and ∑n（logn｜）b/｜n｜（log｜n｜）^d-1P（｜Sn/Vn｜≥ε√log n）,as ε↓0,is established.

On the Strong Laws for Weighted Sums of m-negatively Asso ciated Random Variables

In this article, the author establishes the strong laws for linear statistics that are weighted sums of a m-negatively associated(m-NA) random sample. The obtained results extend and improve the result of Qiu and Yang in [1] to m-NA random variables.

SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].

On the strong convergence properties for weighted sums of negatively orthant dependent random variables

In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent(NOD) random variables are investigated. Let {X, n ≥ 1}be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.

Reliability analysis for aeroengine turbine disc fatigue life with multiple random variables based on distributed collaborative response surface method

The fatigue life of aeroengine turbine disc presents great dispersion due to the randomness of the basic variables,such as applied load,working temperature,geometrical dimensions and material properties.In order to ameliorate reliability analysis efficiency without loss of reliability,the distributed collaborative response surface method(DCRSM) was proposed,and its basic theories were established in this work.Considering the failure dependency among the failure modes,the distributed response surface was constructed to establish the relationship between the failure mode and the relevant random variables.Then,the failure modes were considered as the random variables of system response to obtain the distributed collaborative response surface model based on structure failure criterion.Finally,the given turbine disc structure was employed to illustrate the feasibility and validity of the presented method.Through the comparison of DCRSM,Monte Carlo method(MCM) and the traditional response surface method(RSM),the results show that the computational precision for DCRSM is more consistent with MCM than RSM,while DCRSM needs far less computing time than MCM and RSM under the same simulation conditions.Thus,DCRSM is demonstrated to be a feasible and valid approach for improving the computational efficiency of reliability analysis for aeroengine turbine disc fatigue life with multiple random variables,and has great potential value for the complicated mechanical structure with multi-component and multi-failure mode.

On the Strong Rates of Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables

A general result on the strong convergence rate and complete convergence for arrays of rowwise extended negatively dependent random variables is established. As applications, some well-known results on negatively dependent random variables can be easily extended to the case of arrays of rowwise extended negatively dependent random variables.

The Strong Convergence Properties for Partial Sums of m-NA Random Variables

In this paper, by the three series theorem of m-negatively associated(m-NA,in short) random variables and the truncation method of random variables, we mainly investigated the strong convergence properties for partial sums of m-NA random variables.In addition, the Khintchine-Kolmogorov convergence theorem and Kolmogorov-type strong law of large numbers for m-NA random variables are also obtained. The results obtained in the paper generalize some corresponding ones for independent random variables and some dependent random variables.