MARKOV_CHAIN

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Spectral Gap for Open Jackson Networks被引量：1
《Acta Mathematica Sinica,English Series》2015年第12期1879-1894,共16页Yong Hua MAO Liang Hui XIA 
Supported in part by 985 Project;973 Project(Grant No.2011CB808000);NSFC(Grant No.11131003);SRFDP(Grant No.20100003110005);the Fundamental Research Funds for the Central Universities
We generalize the decomposition method of the finite Markov chains for Poincare inequality in Jerrum et al.（Ann.Appl.Probab.,14,1741-1765（2004）） to the reversible continuous-time Markov chains.And inductively,we g...
关键词：Jackson networks REVERSIBILITY decomposition of Markov chain spectral gap SYMMETRIZATION 
Criterion of Semi-Markov Dependent Risk Model
《Acta Mathematica Sinica,English Series》2014年第7期1273-1280,共8页Xiao Yun MO Xiang Qun YANG 
Supported by National Natural Science Foundation of China(Grant Nos.11171101 and 11271121);Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP)(Education Ministry of China,Hu’nan Normal University),Science and Technology Program of Hu’nan Province(Grant No.2014FJ3058);Scientific Research Fund of Hu’nan Provincial Education Department(Grant No.12C0562);Leading Academic Discipline Project of Hu’nan University of Finance and Economics
A rigorous definition of semi-Markov dependent risk model is given. This model is a generalization of the Markov dependent risk model. A criterion and necessary conditions of semi- Markov dependent risk model are obta...
关键词：Semi-Markov dependent risk model Markov dependent risk model CRITERION necessarycondition Markov chain 
Some Results Associated with the Longest Run in a Strongly Ergodic Markov Chain
《Acta Mathematica Sinica,English Series》2013年第10期1939-1948,共10页Ya Zhe ZHANG Xian Yuan WU 
This paper discusses the asymptotic behaviors of the longest run on a countable state Markov chain. Let {Xa}a∈Z＋ be a stationary strongly ergodic reversible Markov chain on countable- state space S = {1, 2,...}. Let...
关键词：Longest run Stein-Chen method Poisson approximation 
On First Returning Time and Last Exit Time of a Class of Markov Chain
《Acta Mathematica Sinica,English Series》2013年第2期331-344,共14页Hui Zeng ZHANG Min Zhi ZHAO Lei WANG 
Supported by National Natural Science Foundation of China(Grant Nos.11001070,11101113);Zhejiang Provincial Natural Science Foundation(Grant No.R6090034)
Let {Xn} be a Markov chain with transition probability pij =： aj-（i-1）＋,i,j ≥ 0, where aj=0 providedj 〈 0, a0 〉 0, a0＋a1〈 1 and ∑∞n=0 an= 1. Let μ∑∞n=1nan. It is known that {Xn} is positive recurrent wh...
关键词：Geom/G/1 queuing model first returning time last exit time Markov chain 
Markov Chain-based Degree Distributions of Evolving Networks被引量：2
《Acta Mathematica Sinica,English Series》2012年第10期1981-1994,共14页Xiang Xing KONG Zhen Ting HOU Ding Hua SHI Quan Rong CHEN Qing Gui ZHAO 
Supported by National Natural Science Foundation of China (Grant No. 10901164);Graduate Research Innovation Projects in Hunan Province (Grant No. CX2009B020);Graduate Degree Thesis Innovation Foundation of Central South University (Grant No. 2009ybfz11);supported by Natural Science Foundation of China (Grant Nos. 11071258, 90820302);Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090162110058)
In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a correspond...
关键词：Evolving network Markov chain scale-free network degree distribution 
Ergodicity of Quasi-birth and Death Processes(Ⅰ)被引量：1
《Acta Mathematica Sinica,English Series》2007年第2期201-208,共8页Zhen Ting HOU Xiao Hua LI 
partially supported by NSFC(No.10171009);Research Fund for PhD Programs of MOE of China(No.20010533001);Research Fund for Educational Innovation for Doctorates of CSU(No.030602)
Quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the st...
关键词：ERGODICITY quasi-birth and death process Markov chain matrix geometric solutions 
The Invariance Principle for p-■Chain被引量：1
《Acta Mathematica Sinica,English Series》2007年第1期41-56,共16页Di He HU Zheng Yan XIAO 
the NNSF of China(No:10371092)
There are two parts in this paper. In the first part we construct the Markov chain in random environment（MCRE）, the skew product Markov chain and p-θ^→ chain from a random transition matrix and a two-dimensional p...
关键词：random transition matrix Markov chain in random environment skew product Markov chain p-θ^→ chain invariance principle 
Occupation Measures of Singularly Perturbed Markov Chains with Absorbing States被引量：3
《Acta Mathematica Sinica,English Series》2000年第1期161-180,共20页G.Yin~(1)) Department of Mathematics,Wayne State University,Detroit,MI 48202,USAQ.Zhang~(2)) Department of Mathematics,University of Georgia,Athens,GA 30602,USAG.Badowski~(3)) Department of Mathematics,Wayne State University,Detroit,MI 48202,USA 
This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing states.It focuses on both unscaled and scaled occupation measures.Under mild conditions,a mean-square estimat...
关键词：Singularly perturbed Markov chain Occupation measure AGGREGATION Absorbing state Weak convergence Switching diffusion 
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