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CONVERGENCE ON RANDOMLY TRIMMED SUMS WITH A DEPENDENT SAMPLE

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Chinese Annals of Mathematics,Series B 1998年第3期19卷 281-292页

作者： lin zhengyan Hangzhou Univ Dept Math Hangzhou 310028 Peoples R China

Let{X n}be a sequence of random variables and X n1X n2…X nn their order *** this paper a central limit theorem and a strong law of large numbers for randomly trimmed sums T n=βn i=αn+1 X ni are established in the case thatαn andβn are positive integer-valued random variables such thatαn/n andβn/n converge to random variablesαandβrespectively with 0α<β1 in certain sense,and{X n}is aφ-mixing sequence.

关键词： Randomly trimmed sums φmixing a.s.convergence Asymptotic normality

The Limiting Behavior for Observations That Change with Time

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Chinese Annals of Mathematics,Series B 2007年第1期28卷 123-134页

作者： Xiuyun WANG zhengyan lin Department of Mathematics Zheiiang University Xixi Campus Hangzhou 310028 China

Consider a system where units have random magnitude entering according to a homogeneous or nonhomogeneous Poisson process, while in the system, a unit＇s magnitude may change with time. In this paper, the authors obta... 详细信息

关键词： Stochastic system Strong laws of large numbers Random weighted sums Poisson process

A Functional LIL for m-Fold Integrated Brownian Motion

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Chinese Annals of Mathematics,Series B 2006年第4期27卷 459-472页

作者： Rongmao ZHANG zhengyan lin Department of Mathematics Zhejiang University （Xixi Campus） Hangzhou 310028 China School of Mathematical Sciences Peking University Beijing 100871 China. Department of Mathematics Zhejiang University （Xixi Campus） Hangzhou 310028 China.

Let {Xm（t）, t∈R＋} be an m-Fold integrated Brownian motion. In this paper, with the help of small ball probability estimate, a functional law of the iterated logarithm （LIL） for Xm（t） is established. This extends the classic Chung type liminf result for this process. Furthermore, a result about the weighted occupation measure for Xm（t） is also obtained.

关键词： m-Fold integrated Brownian motion Functional law of the integrated logarithm Small ball probability Weighted occupation measure

Some path properties of generalized Lévy sheet

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Science China Mathematics 2006年第12期49卷 1777-1787页

作者： ZHANG Rongmao lin zhengyan Department of Mathematics Zhejiang UniversityHangzhou 310027China Department of MathematicsZhejiang UniversityHangzhou 310027China

Let X(t) be an N parameter generalized Levy sheet taking values in Rd with a lower index a, R={(s,t] =∏i=1N(si,ti)],si 详细信息

Let X(t) be an N parameter generalized Levy sheet taking values in Rd with a lower index a, R={(s,t] =∏i=1N(si,ti)],si

关键词： Lévy sheet,local time,image,increment,Hausdorff dimension.

Increments and sample path properties of Gaussian processes

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Chinese Science Bulletin 1999年第18期44卷 1633-1641页

作者： zhengyan lin Lixin Zhang Zhejiang Univ Dept Math Hangzhou 310028 Peoples R China

The latest results in the field on increments and sample path properties of Gaussian processes are introduced.

关键词： Gaussian process increments sample path property moduli of continuity.

Strong approximation for ρ-mixing sequences

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Science China Mathematics 2012年第10期55卷 2159-2182页

作者： lin zhengyan ZHAO YueXu Department of Mathematics Zhejiang University Hangzhou 310027 China

We establish strong invariance principles for sums of stationary p-mixing random variables with finite and infinite second moments under weaker mixing rates. Some earlier results are improved. As applications, some results of the law of the iterated logarithm with finite and infinite variance are obtained, also a conjecture raised by Shao in 1993 is solved

关键词： strong approximation mixing sequence mixing rate infinite variance martingale

Consistency of kernel density estimators for causal processes

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Science China Mathematics 2014年第5期57卷 1083-1108页

作者： lin zhengyan ZHAO YueXu Department of Mathematics Zhejiang University

Using the blocking techniques and m-dependent methods,the asymptotic behavior of kernel density estimators for a class of stationary processes,which includes some nonlinear time series models,is ***,the pointwise and uniformly weak convergence rates of the deviation of kernel density estimator with respect to its mean(and the true density function)are ***,the corresponding strong convergence rates are *** is showed,under mild conditions on the kernel functions and bandwidths,that the optimal rates for the *** models are also optimal for these processes.

关键词： kernel density estimator consistency rate dependent measure causal process

Empirical likelihood inference for diffusion processes with jumps

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Science China Mathematics 2010年第7期53卷 1802-1813页

作者： lin zhengyan Wang HanChao Zhejiang Univ Dept Math Hangzhou 310027 Peoples R China

In this paper, we consider the empirical likelihood inference for the jump-diffusion model. We construct the confidence intervals based on the empirical likelihood for the infinitesimal moments in the jump-diffusion models. They are better than the confidence intervals which are based on the asymptotic normality of point estimates.

关键词： empirical likelihood N-W estimator jump-diffusion model

The invariance principle for fractionally integrated processes with strong near-epoch dependent innovations

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Science China Mathematics 2011年第1期54卷 117-132页

作者： QIU Jin lin zhengyan School of Mathematics and Statistics Zhejiang University of Finance and Economics Hangzhou 310018 China Department of Mathematics Zhejiang University Hangzhou 310028 China

In this paper, we show the invariance principle for the partial sum processes of fractionally integrated processes, otherwise known as I(d + m) processes, where |d| < 1/2 and m is a nonnegative integer, with strong near-epoch dependent innovations. The results are applied to the test of unit root. The conditions given improve previous results in the literature concerning fractionally integrated processes.

关键词： near-epoch dependence strong near-epoch dependence invariance principle fractionally integrated processes