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Functional central limit theorem for super α-stable processes

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Science china mathematics 2004年第6期47卷 874-881页

作者： HONG WenmingDepartment of mathematics, beijing normal university, beijing 100875, china Department of mathematics Beijing Normal University Beijing China

A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α < d < 2α (0 < α ≤ 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d < 2α, the limiting process is Brownian motion.

关键词： super α-stable processes occupation time central limit theorem evolution equation

On asymptotics of t-type regression estimation in multiple linear model

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Science china mathematics 2004年第4期47卷 628-639页

作者： GUI HengjianDepartment of mathematics, beijing normal university, beijing 100875, china Department of mathematics Beijing Normal University Beijing China

We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error *** marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.

关键词： t-type regression estimator, M-estimator, one-step estimate, consistency, asymptotic normality.

THE HAUSDORFF MEASURE FOR THE SAMPLE PATH OF THE WESTWATER PROCESS

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Chinese Annals of mathematics,Series B 1996年第3期17卷 375-388页

作者： ZHOU XIANYIN(Depatment of mathematics, beijing normal university beijing 100875, china) Department of mathematics Beijing Normal University Beijing 100875 China

It is proved that φ(s) = s2 log |logs| is the correct function to give the Hausdorff measureof a sample path of the Westwater process.

关键词： Hausdorff measure Wiener process Westwater process Sojourn time

SINGLE BIRTH PROCESSES

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Chinese Annals of mathematics,Series B 1999年第1期20卷 77-82页

作者： CHEN MUFA(Department of mathematics,beijing normal university,beijing 100875,china) Department of mathematics Beijing Normal University Beijing 100875 China

The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2 (this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied

关键词： Markov chains Single birth process Uniqueness criterion

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Saturated models

Chinese Science Bulletin 1998年第7期43卷 562-564页

作者： CHEN Guolong Department of mathematics, beijing normal university, beijing 100875, china Department of mathematics Beijing Normal University Beijing China

An equivalent description of saturated models is given, and some properties of countable saturated models, almost saturated models and full models are discussed. New proofs of two important theorems of the related doc... 详细信息

关键词： almost saturated model full model power type.

Recovery of functions via their irregular sampling values

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Chinese Science Bulletin 1998年第4期43卷 268-271页

作者： FANG Gensun Department of mathematics, beijing normal university, beijing 100875, china Department of mathematics Lkijing Normal University Beijing China

It is proved that if a function can be completely reconstructed by tempered splines which satisfy the real Kiesz basis condition as the degree of spline goes to infinity, then the function is band limited.

关键词： band limited function cardinal splines irregular sampling.

Eigenvalues, inequalities and ergodic theory

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Chinese Science Bulletin 2000年第9期45卷 769-774页

作者： CHEN MufaDepartment of mathematics, beijing normal university, beijing 100875, china Department of mathematics Beijing Normal University Beijing China

This paper surveys the main results obtained during the period 1992-1999 on three aspects mentioned in the title. The first result is a new and general variational formula for the lower bound of spectral gap (i.e. the first non-trivial eigenvalue) of elliptic operators in Euclidean space, Laplacian on Riemannian manifolds or Markov chains (?). Here, a probabilistic method -coupling method is adopted. The new formula is a dual of the classical variational formula. The last formula is actually equivalent to Poincare inequality. To which, there are closely related logarithmic Sobolev inequality, Nash inequality, Liggett inequality and so on. These inequalities are treated in a unified way by using Cheeger’s method which comes from Riemannian geometry. This consists of ?2. The results on these two aspects are mainly completed by the author joint with F. Y. Wang. Furthermore, a diagram of the inequalities and the traditional three types of ergodicity is presented (?3). The diagram extends the ergodic

关键词： eigenvalue inequality ergodic theory Markov process.

Coupling, spectral gap and related topics (Ⅱ)

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Chinese Science Bulletin 1997年第18期42卷 1409-1416页

作者： CHEN Muf aDepartment of mathematics, beijing normal university, beijing 100875, china Department of mathematics Beijing Normal University Beijing China

THIS is the second one of a series of three reviews. The ideas introduced in the last review are used to study the estimate of spectral gap and four classes of typical eigenvalue problems on manifolds. The comparison ... 详细信息

关键词： diffusions manifold Markov chains spectral gap couplings.

ON THE RANGE OF RANDOM WALKS IN RANDOM ENVIRONMENT　

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Chinese Annals of mathematics,Series B 1995年第1期16卷 131-138页

作者： ZHOU XIANYIN(Department of mathematics, beijing normal university, beijing 100875, china.) 北京师范大学北京 100875

The range of random walk on Z￣d in symmetric random environment is investigated. As results, it is proved that the strong law of large numbers for the range of random walk on Zdin some random environments holds if d... 详细信息

关键词： Law of large numbers Ergodic theorem Range of random walk Random environment Effective resistance.