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The Birth–death Processes with Regular Boundary: Stationarity and Quasi-stationarity

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Acta Mathematica Sinica,English Series 2022年第5期38卷 890-906页

作者： Wu Jun GAO yong hua mao Chi ZHANG College of Big Data and Internet Shenzhen Technology UniversityShenzhen 518118P.R.China School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex SystemsMinistry of EducationBeijing 100875P.R.China College of Mathematical Sciences Ocean University of ChinaQingdao 266100P.R.China

For the birth–death Q-matrix with regular boundary,its minimal process and its maximal process are closely *** this paper,we obtain the uniform decay rate and the quasi-stationary distribution for the minimal *** via the construction theory,we mainly derive the eigentime identity and the distribution of the fastest strong stationary time(FSST)for the maximal process.

关键词： Birth-death process regular boundary eigenvalue hitting time strong stationary time quasi-stationary distribution

Variational Principles for Asymptotic Variance of General Markov Processes

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Acta Mathematica Sinica,English Series 2023年第1期39卷 107-118页

作者： Lu Jing huaNG yong hua mao Tao WANG School of Mathematics and Statistics Fujian Normal UniversityFuzhou 350007P.R.China School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex SystemsMinistry of EducationBeijing 100875P.R.China

A variational formula for the asymptotic variance of general Markov processes is *** application,we get an upper bound of the mean exit time of reversible Markov processes,and some comparison theorems between the reve... 详细信息

关键词： Markov process asymptotic variance variational formula the mean exit time comparison theorem semi-Dirichlet form

On the Empty Essential Spectrum for Markov Processes in Dimension One

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Acta Mathematica Sinica,English Series 2006年第3期22卷 807-812页

作者： yong hua mao Department of Mathematics Beijing Normal University

This paper gives characterizations for diffusion processes on the line and birth-death processes whose generators admit the empty essential spectra. Some equivalent conditions for empty essential spectra for general M... 详细信息

关键词： Markov generator Essential spectrum Compact embedding Hardy-type inequality

On Supercontractivity for Markov Semigroups

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Acta Mathematica Sinica,English Series 2007年第5期23卷 905-914页

作者： yong hua mao School of Mathematical Science Beijing Normal University Beijing 100875 P. R. China

In this paper, we study the supercontractivity for Maxkov semigroups and obtain some sufficient and necessary conditions; especially explicit formulae are obtained for birth-death process and diffusion on the line. Sufficient conditions and necessary conditions in terms of isoperimetric inequalities are also presented. Moreover, we prove that the supercontractivity is equivalent to the compact embedding of Sobolev space into an Orlicz space.

关键词： Markov semigroup logarithmic Sobolev inequality supercontractivity compact embedding

L^P-Poincaré Inequality for General Symmetric Forms

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Acta Mathematica Sinica,English Series 2009年第12期25卷 2055-2064页

作者： yong hua mao School of Mathematical Science LMCS Ministing of Education Beijing Normal University Beijing 100875 P. R. China

Lp Poincare inequalities for general symmetric forms are established by new Cheeger＇s isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact embedding, and the criteria via the new Cheeger＇s constants for those inequalities are presented. Finally, the concentration or the volume growth of measures for these inequalities are studied.

关键词： Lp Poincare inequality symmetric form isoperimetric constant compact embedding concentration

Construction of Generalized Diffusion Processes: the Resolvent Approach

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Acta Mathematica Sinica,English Series 2020年第6期36卷 691-710页

作者： Ying LI yong hua mao School of Mathematics and Computational Science Xiangtan UniversityXiangtan 411105P.R.China School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex SystemsMinistry of EducationBeijing 100875P.R.China

In this paper,we define the generalized diffusion operator L=d/dMd/dS for two suitable measures on the line,which includes the generators of the birth-death processes,the one-dimensional diffusion and the gap diffusio... 详细信息

关键词： Generalized diffusion operator birth-death processes diffusion gap diffusion resolvent generalized diffusion processes

The Spectral Gap for Quasi-birth and Death Processes

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Acta Mathematica Sinica,English Series 2012年第5期28卷 1075-1090页

作者： yong hua mao Liang Hui XIA School of Mathematical Sciences LMCSMinistry of EducationBeijing Normal University Department of Mathematics Ji'nan University

For a reversible quasi-birth and death process, we generalize and refine the decomposition method, by constructing a birth-death process and a sequence of restriction processes. The spectral gap for the quasi-birth and death process is estimated in terms of the spectral gaps for these processes, and in some special cases, the estimation is sharp. With the aid of the symmetrization procedure, the result is also applied to two queueing models： M/M/1 in random environment and MIMIc with synchronous vacation.

关键词： Quasi-birth and death process spectral gap birth-death process M/M/1 in random environment MIMIc with synchronous vacation

Spectral Gap and Convergence Rate for Discrete-time Markov Chains

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Acta Mathematica Sinica,English Series 2013年第10期29卷 1949-1962页

作者： yong hua mao Yan Hong SONG School of Mathematical Sciences LMCSMinistry of EducationBeijing Normal University

Abstract Let P be a transition matrix which is symmetric with respect to a measure π. The spectral gap of P in L2（π）-space, denoted by gap（P）, is defined as the distance between 1 and the rest of the spectrum of P. In this paper, we study the relationship between gap（P） and the convergence rate of P^n. When P is transient, the convergence rate of pn is equal to 1 - gap（P）. When P is ergodic, we give the explicit upper and lower bounds for the convergence rate of pn in terms of gap（P）. These results are extended to L^∞ （π）-space.

关键词： Spectral gap convergence rate geometric ergodicity transience strong ergodicity uni-form decay

Spectral Gap for Open Jackson Networks

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Acta Mathematica Sinica,English Series 2015年第12期31卷 1879-1894页

作者： yong hua mao Liang Hui XIA School of Mathematical Sciences LMCSMinistry of Education Beijing Normal University Department of Mathematics Ji'nan University

We generalize the decomposition method of the finite Markov chains for Poincare inequality in Jerrum et al.（***.,14,1741-1765（2004）） to the reversible continuous-time Markov *** inductively,we give the lower bound of spectral gap for the ergodic open Jackson network by the decomposition method and the symmetrization *** upper bound of the spectral gap is also presented.

关键词： Jackson networks reversibility decomposition of Markov chain spectral gap symmetrization