检索结果-南通市图书馆

SINGLE BIRTH PROCESSES

在线全文

学校读者我要写书评

暂无评论

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) beijing normal Univ Dept Math Beijing 100875 Peoples R 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

The Principal Eigenvalue for Jump Processes

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2000年第3期16卷 361-368页

作者： Mufa chen department of mathematics,beijing normal university,beijing 100875.P.R.china department of mathematics Beijing Normal University Beijing 100875 P. R. China

A variational formula for the lower bound of the principal eigenvalue of general Markov jump processes is *** result is complete in the sense that the condition is fulfilled and the resulting bound is sharp for Markov... 详细信息

关键词： Principal eigenvalue Jump processes Variational formula for Dirichlet form

Variational Formulas of Poincare-Type Inequalities in Banach Spaces of Functions on the Line

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2002年第3期18卷 417-436页

作者： Mu Fa chen department of mathematics. beijing normal. university. beijing 100875. P. R. china department of mathematics Beijing Normal University Beijing P. R. China

Motivated from the study on logarithmic Sobolev. Nash and other functional inequalities, the variational formulas for Poincare inequalities are extended to a large class of Banach (Orlicz) spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimates for the optimal constants in the inequalities are presented. As a typical application, the logarithmic Sobolev constant is carefully examined.

关键词： Variational formula Poincare inequality Logarithmic Sobolev inequality Orliez space

Nash Inequalities for General Symmetric Forms

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 1999年第3期15卷 353-370页

作者： Mufa chen department of mathematics, beijing normal university, beijing 100875. P. R. china department of mathematics Beijing Normal University Beijing P. R. China

This paper deals with the Nash inequalities and the related ones for general symmetric forms which can be very much unbounded. Some sufficient conditions in terms of the isoperimetric inequalities and some necessary conditions for the inequalities are presented. The resulting conditions can be sharp qualitatively as illustrated by some examples. It turns out that for a probability measure, the Nash inequalities are much stronger than the Poincare and the logarithmic Sobolev inequalities in the present context.

关键词： Nash inequality Symmetric form Isoperimetric Inequality Jump process

Optimal Markovian Couplings and Applications

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 1994年第3期10卷 260-275页

作者： chen Mufa department of mathematics beijing normal university beijing,100875.china 1. department of mathematics Beijing Normal University 100875 Beijing China

This paper is devoted to studying a new topic:optimal Markovian couplings,mainly for time-continuous Markov *** study emphasizes the analysis of the coupling opera- tors rather than the *** constructions of optimal Markovian couplings for Markov chains and diffusions are presented,which are often ***,the results are applied to study the L^2-convergence for Markov chains and for a diffusion on compact *** estimate of the convergent rate provided by this method can be sharp.

关键词： chen Optimal Markovian Couplings and Applications OMC

Eigenvalues, inequalities and ergodic theory

在线全文

学校读者我要写书评

暂无评论

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.

Estimate of Exponential Convergence Rate in Total Variation by Spectral Gap

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 1998年第1期14卷 9-16页

作者： chen Mufa department of mathematics, beijing normal university, beijing 100875. china 北京师范大学数学系北京

This note is devoted to study the exponential convergence rate in the total variation for reversible Markov processes by comparing it with the spectral gap. It is proved that in a quite general setup, with a suitable restriction on the initial distributions, the rate is bounded from below by the spectral gap. Furthemore, in the compact case or for birth-death processes or half-line diffosions, the rate is shown to be equal to the spectral gap.

关键词： Total variation Spectral gap Markov processes

Estimation of Spectral Gap for Markov Chains

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 1996年第4期12卷 337-360页

作者： chen Mufa department of mathematics beijing normal university beijing, 100875.china department of mathematics Beijing Normal University Beijing China

The study of the convergent rate (spectra gap) in the L^2-sense is motivated from several different fields: probability statistics, mathematical physics, computer science and so on and it is now an artive research topic. Based on a new approach (the coupling technique) introduced in [7] for the estimate of the convergent rate and as a continuation of [4],[5],[7-9],[23] and [24], this paper studies the estimate of the rate for time-continuous Markov chains. Two variational formulas for the rate are presented here for the first time for birth-death processes. For diffusions, similar results are presented in an accompany paper [10]. The new formulas enable us to recover or improve the main known results. The connection between the sharp estimate and the corresponding eigenfunction is explored and illustrated by various examples. A previous result on optimal Markovian couplings is also extended in the paper.

关键词： Markov chains Spectral gap Couplings

Coupling, spectral gap and related topics (Ⅱ)

在线全文

学校读者我要写书评

暂无评论

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 100875 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.