Frontiers of Mathematics in China >

2014 , Vol. 9 >Issue 5: 1033 - 1049

DOI: https://doi.org/10.1007/s11464-014-0386-2

RESEARCH ARTICLE

L2-Decay rate for non-ergodic Jackson network

  • Huihui CHENG 1 ,
  • Yonghua MAO , 2
Expand
  • 1. School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450045, China
  • 2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Received date: 21 Feb 2011

Accepted date: 08 May 2014

Published date: 26 Aug 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
Fold

Abstract

We establish the additive theorem of L2-decay rate for multidimensional Markov process with independent marginal processes. Using this and the decomposition method, we obtain explicit upper and lower bounds for decay rate of non-ergodic Jackson network. In some cases, we get the exact decay rate.

Key words： L2-Decay rate; additive theorem; decomposition method; Jackson network

Cite this article

Huihui CHENG , Yonghua MAO . L2-Decay rate for non-ergodic Jackson network[J]. Frontiers of Mathematics in China, 2014 , 9(5) : 1033 -1049 . DOI: 10.1007/s11464-014-0386-2

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Chen M F. Equivalence of exponential ergodicity and L2-exponential convergence for Markov chains. Stochastic Process Appl, 2000, 87(2): 281-297

DOI

2
Chen M F. Explicit bounds of the first eigenvalues. Sci China Ser A, 2000, 43: 1051-1059

DOI

3
Chen M F. From Markov Chains to Non-equilibrium Particle Systems. Singapore: World Scientific, 2004

4
Chen M F. Speed of stability for birth-death processes. Front Math China, 2010, 5(3): 379-515

DOI

5
Chen M F, Mao Y H. An Introduction to Stochastic Processes. Beijing: Higher Education Press, 2007 (in Cinese)

6
van Doorn E A. Conditions for exponential ergodicity and bounds for the decay parameter of a birth-death process. Adv Appl Probab, 1985, 17(3): 514-530

DOI

7
Goodman J M, Massey W A. The non-ergodic Jackson network. J Appl Probab, 1984, 21: 860-869

DOI

8
Jackson J R. Networks of waiting lines. Oper Res, 1957, 5: 518-521

DOI

9
Jackson J R. Jobshop-like queuing systems. Manag Sci, 1963, 10: 131-142

DOI

10
Jerrum M, Son J B, Tetali P, Vigoda E. Elementary bounds on Poincaré and log-Sobolev constant for decomposable Markov chains. Ann Appl Probab, 2004, 14: 1741-1765

DOI

11
Kelbert M Ya, Kontsevich M L, Rybko A N. On Jackson networks on countable graphs. Veroyatn Primen, 1988, 33: 379-382

12
Mao Y H. Nash inequalities for Markov processes in dimension on<?Pub Caret?>e. Acta Math Sin (Engl Ser), 2002, 18(1): 147-156

DOI

13
Mao Y H. General Sobolev type inequalities for symmetric forms. J Math Anal Appl, 2008, 33: 1092-1099

DOI

14
Mao Y H. Lp Poincaré inequality for general symmetric forms. Acta Math Sin (Engl Ser), 2009, 25: 2055-2064

DOI

15
Mao Y H, Ouyang S X. Strong ergodicity and uniform decay for Markov processes. Math Appl (Wuhan), 2006, 19(3): 580-586

16
Mao Y H, Xia L H. Spectral gap for jump processes by decomposition method. Front Math China, 2009, 4(2): 335-348

DOI

17
Mao Y H, Xia L H. The specrtal gap for quasi-birth and death processes. Acta Math Sin (Engl Ser), 2012, 28(5): 1075-1090

DOI

18
Mao Y H, Xia L H. Spectral gap for open Jackson networks. 2012, Preprint

19
Meyn S, Tweedie R L. Markov Chains and Stochastic Stability. London: Springer-Verlag, 1993

DOI

20
Wang F Y. Functional inequalities for the decay of sub-Markov semigroups. Potential Anal, 2003, 18: 1-23

DOI

21
Wang F Y. Functional Inequalities, Markov Semigroups and Spectral Theory. Beijing: Science Press, 2005

22
Yau S T, Schoen R. Lectures on Differential Geometry. Beijing: Higher Education Press, 2004 (in Chinese)

Options
Outlines

/

〈 〉