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A general result on precise asymptotics for linear processes of positively associated sequences

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Applied Mathematics(A Journal of Chinese Universities) 2008年第2期23卷 190-196页

作者： TAN Xi-li YANG Xiao-yun Dept. of Math Beihua Univ. Jilin 132013 China Institute of Math. Jilin Univ.（Qianwei Campus） Changchun 130012 China

Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers satisfying ∑j=0^∞｜aj｜〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥*** that E｜ε1｜^2＋δ′〈 for some δ′〉0 and μ（n）=O（n^-ρ） for some ρ〉*** paper achieves a general law of precise asymptotics for {Sn}.

关键词： PA sequence linear process general law precise asymptotics.

Central limit theolrem for linear processes generated byⅡD random variables under the sub-linear expectation

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Applied Mathematics(A Journal of Chinese Universities) 2021年第2期36卷 243-255页

作者： LIU Wei ZHANG Yong School of Mathematics Jilin UniversityChangchun 130012China

In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expectations initiated by Peng[19].It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's central limit theorem and invariance principle to the case where probability measures are no longer additive.

关键词： central limit theorem invariance principle ⅡD random variables sub-linear expectation linear process

The Invariance Principle for linear processes Generated by a Negatively Associated Sequence and Its Applications

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Acta Mathematicae Applicatae Sinica 2003年第4期19卷 641-646页

作者： Chuan-rong LuZhejiang University of Finance and Economics, Hongzhou 310012. China Zhejiang University of Finance and Economics Hangzhou 310012

In this paper, we obtain the invariance principle for linear processes generated by a negatively associated sequence.

关键词： linear process Negatively associated sequence Weak convergence

Hajek-Rényi-type Inequality and Strong Law of Large Numbers for Some Dependent Sequences

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Acta Mathematicae Applicatae Sinica 2012年第3期28卷 495-504页

作者： Wen-zhi YANG Yan SHEN Shu-he HU Xue-jun WANG School of Mathematical Science Anhui UniversityHefei 230039China

Abstract In this paper, we get the H^jek-R^nyi-type inequalities for a pairwise NQD sequence, an L^T （r 〉 1） mixingale and a linear process, which have the concrete coefficients. In addition, we obtain the strong law of large numbers, strong growth rate and the integrability of supremum for the above sequences, which generalize and improve Corollary 2 for L^T（r 〉 1） mixingale of Hansen.

关键词： Hajek-Renyi-type inequality pairwise NQD sequence L^r(r 〉 1) mixingale linear process

LARGE DEVIATIONS FOR SOME DEPENDENT SEQUENCES

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Acta Mathematica Scientia 2008年第2期28卷 295-300页

作者：胡舒合王学军 School of Mathematics and Computation Science Anhui University

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.

关键词： Large deviation φ-mixing sequence NA sequence linear process

STRONG APPROXIMATION FOR MOVING AVERAGE processES UNDER DEPENDENCE ASSUMPTIONS

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Acta Mathematica Scientia 2008年第1期28卷 217-224页

作者：林正炎李德柜 Department of Mathematics Zhejiang University

Let {Xt,t ≥ 1} be a moving average process defined by Xt = ∑^∞ k=0 αkξt-k, where {αk,k ≥ 0} is a sequence of real numbers and {ξt,-∞ 〈 t 〈 ∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {αk, k ≥ 0} which entail that {Xt, t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt, t ≥ 1} to a Gaussian process is studied. Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.

关键词： Strong approximation long memory process linear process fractional Brownian motion the law of the iterated logarithm

Functional limit theorem for moving average processes generated by dependent random variables

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Progress in Natural Science:Materials International 2006年第3期16卷 266-273页

作者： LIN Zhengyan and LI Degui (Department of Mathematics, Zhejiang University, Hangzhou 310028, China) [a]Department of Mathematics Zhejiang University Hangzhou China

Let {Xt,t≥1} be a moving average process defined by , where {bj,j≥0} is a sequence of real num- bers and {ξt,-∞ 详细信息

Let {Xt,t≥1} be a moving average process defined by , where {bj,j≥0} is a sequence of real num- bers and {ξt,-∞process or a linear process, we study asymptotics of (properly nor- malized). When {Xt,t≥1} is a long memory process, we establish a functional limit theorem. When {Xt,t≥1} is a linear process, we not only obtain the multi-dimensional weak convergence for {Xx,t≥1},but also weaken the moment condition on {ξt,-∞

关键词： functional limit theorem long memory process linear process moving average process φ-mixing.