Precise Asymptotics in the Baum-Katz and Davis Laws of Large Numbers of ρ-mixing Sequences

Let {X,Xn;n ≥ 1} be a strictly stationary sequence of ρ-mixing random variables with mean zeros and finite variances. Set Sn =∑k=1^n Xk, Mn=maxk≤n｜Sk｜,n≥1.Suppose limn→∞ESn^2/n=：σ^2〉0 and ∑n^∞=1 ρ^2/d（2^n）〈∞,where d=2 if 1≤r〈2 and d〉r if r≥2.We prove that if E｜X｜^r 〈∞,for 1≤p〈2 and r〉p,then limε→0ε^2（r-p）/2-p ∑∞n=1 n^r/p-2 P{Mn≥εn^1/p}=2p/r-p ∑∞k=1（-1）^k/（2k＋1）^2（r-p）/（2-p）E｜Z｜^2（r-p）/2-p,where Z has a normal distribution with mean 0 and variance σ^2.     

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.     

α-混合序列指数不等式及强大数定律

给出了α-混合序列部分和的一个指数不等式,并利用指数不等式证得了α-混合序列的强大数定律及强收敛速度.     

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.     

φ-混合随机变量序列收敛性质的若干新结果

本文将Kolmogorov型不等式推广到φ-混合序列,并且研究其强收敛性质,得到了φ-混合序列的Khintchine-Kolmogorov型收敛定理、三级数定理和Marcitlkiewicz型强大数定律.     

(p)混合序列部分和的强大数定律

设{Xn,n≥1)是(p)混合序列.利用随机变量的板尾方法和(p)混合序列的三级数定理这一工具研究了(p)混合序列的性质.得到了矩条件下(p)混合序列的一类强极限定理和强大数定律.并给出了一些简单应用.推广了若干经典的强大数定律.