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.

A Precise Asymptotic Behaviour of the Large Deviation Probabilities for Weighted Sums

Let {Xn, n ≥ 1} be a sequence of independent and identically distributed positive valued random variables with a common distribution function F. When F belongs to the domain of partial attraction of a semi stable law with index α, 0 < α < 1, an asymptotic behavior of the large deviation probabilities with respect to properly normalized weighted sums have been studied and in support of this we obtained Chover’s form of law of iterated logarithm.

Empirical Likelihood Statistical Inference for Compound Poisson Vector Processes under Infinite Covariance Matrix

The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.

A LIL and Limit Distributions for Trimmed Sums of Random Vectors Attracted to Operator Semi-stable Laws

Let θ∈^d be a unit vector and let X, X1, X2,…… be a sequence of i.i.d. Xd-valued random vectors attracted to operator semi-stable laws. For each integer n ≥1, let X1,≤……≤ Xn,n denote the order statistics of X1, X2,..., Xn according to priority of index, namely ｜（X1,nθ）｜≥…≥ [（Xn,n,θ）1, where （., .） is an inner product on Rd. For all integers r ≥ 0, define by （r）Sn =∑n-r i=1Xi,n the trimmed sum. In this paper we investigate a law of the iterated logarithm and limit distributions for trimmed sums （r）Sn. Our results give information about the maximal growth rate of sample paths for partial sums of X when r extreme terms are excluded. A stochastically compactness of （r）Sn is obtained.

稳定律吸引场中学生化的Hanson-Russo型增量定理

该文通过建立关于部分和学生化增量的大偏差不等式 ,在稳定律吸引场中证得了学生化的 Hanson- Russo型增量定理 .

CHOVER'S LAW OF THE ITERATED LOGARITHM FOR NEGATIVELY ASSOCIATED SEQUENCES

Consider a sequence of negatively associated and identically distributed random variableswith the underlying distribution in the domain of attraction of a stable distribution with an exponentin(0,2).A Chover's law of the iterated logarithm is established for negatively associated randomvariables.Our results generalize and improve those on Chover's law of the iterated logarithm(LIL)type behavior previously obtained by Mikosch(1984),Vasudeva(1984),and Qi and Cheng(1996)fromthe i.i.d,case to NA sequences.

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.

A Self-normalized Law of the Iterated Logarithm for the Geometrically Weighted Random Series

Let {X, Xn; n ≥ 0} be a sequence of independent and identically distributed random variables with EX=0, and assume that EX^2I（｜X｜ ≤ x） is slowly varying as x →∞, i.e., X is in the domain of attraction of the normal law. In this paper, a self-normalized law of the iterated logarithm for the geometrically weighted random series Σ~∞（n=0）β~nXn（0 〈 β 〈 1） is obtained, under some minimal conditions.

Studentized Increments of Partial Sums

Using suitable self-normalization for partial sums of i.i.d.random variables,Griffin and Kuelbs established the law of the iterated logarithm for all distributions in the domain of attraction of a normal law.We obtain the corresponding results for Studentized increments of partial sums under thesame condition.

A strong approximation of self-normalized sums

Let {X,Xn,n1} be a sequence of independent identically distributed random variables with EX=0 and assume that EX2I(|X|≤x) is slowly varying as x→∞,i.e.,X is in the domain of attraction of the normal law.In this paper a Strassen-type strong approximation is established for self-normalized sums of such random variables.

重尾随机变量序列滑动平均过程的极限性质

对分布属稳定分布吸引场的独立同分布随机变量序列的滑动平均过程,用积分检验刻画了其极限性质.作为应用,获得了相应的Chover型重对数律.

关于Chover重对数律

J.Chover(1966)对分布为特征指数为α(0<α<2)的对称稳定分布的独立同分布随机变量序列部分和建立了一个重对数律,本文将此推广到分布属于特征指数为α(0<α<2)的非退化稳定分布的正则吸引场的独立同分布随机变量序列部分和上。

稳定律吸引场中两两NQD列的L^r收敛性

讨论了稳定律吸引场中两两NQD列的Lr收敛性,利用截尾的手法获得了与独立情形相类似的结果.

吸引区估计的V函数方法

对渐近稳定的有关定理作了一些改进 ,在此基础上讨论了平凡解X

单自由度含干摩擦碰振系统相邻周期运动转迁规律分析

以一类单自由度含干摩擦和间隙的碰撞振动系统为研究对象,通过理论计算及数值仿真,分析了系统在参数ω和δ协同变化下周期运动的分布及相邻周期运动之间的转迁规律。根据周期运动的边界条件和衔接条件理论推导得到了系统4-p-1周期运动存在的条件;根据响应微扰积分计算得到系统Floquet矩阵和Lyapunov指数,判断系统的稳定性及分叉;根据系统相轨线与约束面的关系将周期运动划分为四类,结合Lyapunov指数,仿真得到了在参数ω和δ协同变化下系统的周期运动分布图;基于胞映射方法,分析了系统各相邻周期运动经非光滑分岔进行转迁的规律。研究发现,在擦边和鞍结分岔前后伴随着系统相轨迹的Sliding分岔,这是一种特殊的非光滑分岔现象。

稳定分布吸引域的几乎处处中心极限定理

讨论了稳定分布吸引域的几乎处处中心极限定理,把Fredrik Jonsson几乎处处中心极限定理中的权重dk=1/kexp{(lnk)γ}推广到dk=lnak+1/akexp{(lnk)γ}和dk=lnak+1/akexp{(lnak)γ},0≤γ≤12的情形.

一种改进的吸引域估计的方法

在考察具有渐近稳定平衡点的非线性动力系统的时候,其吸引域范围是判断系统稳定性的一类重要指标.利用最优Lyapunovh函数法,可以得到一大类非线性动力系统所对应的Lyapunov函数,并利用该函数对吸引域范围进行估计.基于最优最优Lyapunov函数,通过对原吸引域估计方法进行改进,可以显著提高估计的准确性,得到更好估计结果,并通过数值实验证明了这一点。

方差可能无穷的“中度偏离”单位根过程的复合分位数估计

考虑一类"中度偏离"单位根过程,y_t=q_ny_t-1+u_t,其中qn=1+c/(k_n),k_n=o(n),c为一非零常数,{u_t}为随机扰动项序列.在允许扰动项方差无穷的条件下,构造q_n的复合分位数估计,并得到了该估计的渐近分布.最后通过数值模拟,在扰动项服从t(2)分布下,说明了该估计的稳健和有效性.

算子半稳定分布的正规吸引域

基于算子半稳定分布的概念及满的算子半稳定分布μ的特征,利用μ的对称群刻画出其中的算子B,并给出两个算子半稳定分布的正规吸引域的关系.

稳定分布吸引场中φ-混合随机变量序列加权和的极限性质

有关独立同分布随机变量序列加权和的强大数定律,已经有较完善的结果。近来陈平炎等人又研究了具有稳定分布的独立同分布随机变量序列的加权和的极限性质,而且得出有关(?)-混合随机变量序列的重对数律。本文主要是讨论稳定分布吸引场中(?)-混合序列加权和的极限性质,并给出相应的重对数律。