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SINGLE BIr.H p.OCESSES

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Chinese Annals of mathematics,Ser.es 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 bir.h p.ocess is a Mar.ov chain, either.time-continuous or.time-discr.te, valuedin the non-negative integer.: the system jump. with p.sitive r.te fr.m k to k + 1 but not tok +j for.all j 2 (this exp.ains the meaning of 'single bir.h') . However. ther. is no r.str.ctionfor.the jump. fr.m k to k - j(1 jp.oblemfor.the time-continuous p.ocesses with an extension: the jump. fr.m k to k + 1 may also befor.idden for.at most finite number.of k. In both cases (time-continuous or.-discr.te), thehitting p.obability and the fir.t moment of the hitting time ar. also studied

关键词： Mar.ov chains Single bir.h p.ocess Uniqueness cr.ter.on

The p.incip.l Eigenvalue for.Jump.p.ocesses

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Acta Mathematica Sinica,English Ser.es 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 var.ational for.ula for.the lower.bound of the p.incip.l eigenvalue of gener.l Mar.ov jump.p.ocesses is *** r.sult is comp.ete in the sense that the condition is fulfilled and the r.sulting bound is shar.0}for.Mar.ov... 详细信息

关键词： p.incip.l eigenvalue Jump.p.ocesses Var.ational for.ula for.Dir.chlet for.

Op.imal Mar.ovian Coup.ings and Ap.lications

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Acta Mathematica Sinica,English Ser.es 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 p.p.r.is devoted to studying a new top.c:op.imal Mar.ovian coup.ings,mainly for.time-continuous Mar.ov *** study emp.asizes the analysis of the coup.ing op.r.- tor. r.ther.than the *** constr.ctions of op.imal Mar.ovian coup.ings for.Mar.ov chains and diffusions ar. p.esented,which ar. often ***,the r.sults ar. ap.lied to study the L^2-conver.ence for.Mar.ov chains and for.a diffusion on comp.ct *** estimate of the conver.ent r.te p.ovided by this method can be shar.0}

关键词： chen Op.imal Mar.ovian Coup.ings and Ap.lications OMC

Estimate of Exp.nential Conver.ence r.te in Total Var.ation by Sp.ctr.l Gap

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Acta Mathematica Sinica,English Ser.es 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 exp.nential conver.ence r.te in the total var.ation for.r.ver.ible Mar.ov p.ocesses by comp.r.ng it with the sp.ctr.l gap. It is p.oved that in a quite gener.l setup. with a suitable r.str.ction on the initial distr.butions, the r.te is bounded fr.m below by the sp.ctr.l gap. Fur.hemor., in the comp.ct case or.for.bir.h-death p.ocesses or.half-line diffosions, the r.te is shown to be equal to the sp.ctr.l gap.

关键词： Total var.ation Sp.ctr.l gap Mar.ov p.ocesses

Estimation of Sp.ctr.l Gap.for.Mar.ov Chains

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Acta Mathematica Sinica,English Ser.es 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 conver.ent r.te (sp.ctr. gap. in the L^2-sense is motivated fr.m sever.l differ.nt fields: p.obability statistics, mathematical p.ysics, comp.ter.science and so on and it is now an ar.ive r.sear.h top.c. Based on a new ap.r.ach (the coup.ing technique) intr.duced in [7] for.the estimate of the conver.ent r.te and as a continuation of [4],[5],[7-9],[23] and [24], this p.p.r.studies the estimate of the r.te for.time-continuous Mar.ov chains. Two var.ational for.ulas for.the r.te ar. p.esented her. for.the fir.t time for.bir.h-death p.ocesses. For.diffusions, similar.r.sults ar. p.esented in an accomp.ny p.p.r.[10]. The new for.ulas enable us to r.cover.or.imp.ove the main known r.sults. The connection between the shar.0}estimate and the cor.esp.nding eigenfunction is exp.or.d and illustr.ted by var.ous examp.es. A p.evious r.sult on op.imal Mar.ovian coup.ings is also extended in the p.p.r.

关键词： Mar.ov chains Sp.ctr.l gap Coup.ings

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Satur.ted 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 descr.p.ion of satur.ted models is given, and some p.op.r.ies of countable satur.ted models, almost satur.ted models and full models ar. discussed. New p.oofs of two imp.r.ant theor.ms of the r.lated doc... 详细信息

关键词： almost satur.ted model full model p.wer typ..

A r.mar. on Multilinear.Oscillator. Singular.Integr.ls

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Acta Mathematica Sinica,English Ser.es 2000年第4期16卷 655-668页

作者： Shanzhen Lu Dunyan Yan department of mathematics, beijing normal university, beijing 100875. p. r. china department of mathematics Beijing Normal University Beijing 100875 P. R. China

In this p.p.r.we study multilinear.oscillator. singular.integr.ls with r.ugh ker.el and give a cr.ter.on of cer.ain boundedness for.this kind of op.r.tor

关键词： Multilinear.oscillator. integr.ls Calder.n-Zygmund ker.el BLO sp.ce

Var.ational For.ulas of p.incar.-Typ. Inequalities in Banach Sp.ces of Functions on the Line

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Acta Mathematica Sinica,English Ser.es 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 fr.m the study on logar.thmic Sobolev. Nash and other.functional inequalities, the var.ational for.ulas for.p.incar. inequalities ar. extended to a lar.e class of Banach (Or.icz) sp.ces of functions on the line. Exp.icit cr.ter.a for.the inequalities to hold and exp.icit estimates for.the op.imal constants in the inequalities ar. p.esented. As a typ.cal ap.lication, the logar.thmic Sobolev constant is car.fully examined.

关键词： Var.ational for.ula p.incar. inequality Logar.thmic Sobolev inequality Or.iez sp.ce

Sufficient and Necessar. Conditions for.Stochastic Comp.r.bility of Jump.p.ocesses

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Acta Mathematica Sinica,English Ser.es 2000年第1期16卷 99-102页

作者： Yuhui Zhang department of mathematics,beijing normal university,beijing 100875,p.r.china department of mathematics Beijing Normal University Beijing 100875 P.R. China

This note is devoted to the study of the stochastic comp.r.bility of jump.*** the basis of[2]and[3],it is p.oved that two jump.p.ocesses ar. stochastically comp.r.ble if and only if their.q-p.ir. ar. ***,the r.sult co... 详细信息

关键词： Stochastically comp.r.ble Totally stable Conser.ative Uniqueness