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Ergodicity of Quasi-birth and Death Processes(Ⅰ) 被引量：1

Ergodicity of Quasi-birth and Death Processes(Ⅰ)
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摘要 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 stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for/-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic. Keywords ergodicity, quasi-birth and death process. 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 stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for/-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic. Keywords ergodicity, quasi-birth and death process.
作者 Zhen Ting HOU Xiao Hua LI
机构地区 School of Mathematics School of science
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第2期201-208,共8页 数学学报（英文版）
基金 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)
关键词 ERGODICITY quasi-birth and death process Markov chain matrix geometric solutions ergodicity, quasi-birth and death process, Markov chain, matrix geometric solutions
分类号 O211.6 [理学—概率论与数理统计]
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参考文献14

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  • 2Wallace, V.: The solution of quasi-birth and death processes arising from multiple access computer systems,Ph.D. diss., Systems Engineering Laboratory, University of Michigan, Tech. Rept., no. 07742-6-T, 1969
  • 3Neuts, M.: Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, The Johns Hopkins University Press, Baltimore, 1981
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同被引文献15

  • 1陈木法.Analytic proof of dual variational formula for the first eigenvalue in dimension one[J].Science China Mathematics,1999,42(8):805-815. 被引量：27
  • 2侯振挺,李晓花.拟生灭过程几种遍历性的判别准则(Ⅱ)[J].数学年刊（A辑）,2005,26(2):181-192. 被引量：1
  • 3Mufa Chen.Analytic proof of dual variational formula for the first eigenvalue in dimension one[J].Science in China Series A: Mathematics.1999(8)
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  • 7Naishuo Tian,Zhe George Zhang.A Two Threshold Vacation Policy in Multiserver Queueing Systems[].European Journal of Operational Research.2006
  • 8M. F. Chen.From Markov Chains to Non-equilibrium Particle Systems[]..2004
  • 9G. O. Roberts,R. L. Tweedie.Geometric L 2 and L 1 convergence are equivalent for reversible Markov chains[].Journal of Applied Probability.2001
  • 10Jerrum M,Son J B,Tetall P,Vigoda E.Elementary bounds on Poincare and Log- Sobolev constants for decomposable Markov chains[].Annals of Applied Probability.2004

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Acta Mathematica Sinica,English Series
2007年 第2期

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