Eigentime identity for asymmetric finite Markov chains

Hao Cui; Yong-Hua Mao

doi:10.1007/s11464-010-0067-8

Front. Math. China ›› 2010, Vol. 5 ›› Issue (4) : 623 -634. DOI: 10.1007/s11464-010-0067-8

Research Article

RESEARCH ARTICLE

Eigentime identity for asymmetric finite Markov chains

Hao Cui ¹
, Yong-Hua Mao ¹^,^b

Author information +

History +

PDF (158KB)

Abstract

Two kinds of eigentime identity for asymmetric finite Markov chains are proved both in the ergodic case and the transient case.

Keywords

Asymmetric Markov chain / eigenvalue / hitting time / Jordan decomposition

Cite this article

Download citation ▾

Hao Cui, Yong-Hua Mao. Eigentime identity for asymmetric finite Markov chains. Front. Math. China, 2010, 5(4): 623-634 DOI:10.1007/s11464-010-0067-8

登录浏览全文

4963

注册一个新账户忘记密码

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Aldous D, Fill J. Reversible Markov Chains and Random Walks on Graphs. 2003. URL www.berkeley.edu/users/aldous/book.html

[2]	Aldous D., Thorisson H. Shift coupling. Stoch Proc Appl, 1993, 44: 1-14.

[3]	Anderson W. Continuous-time Markov Chains, 1991, New York: Springer-Verlag.

[4]	Chen G. N. Matrix Theory and Applications, 2007 2nd Ed. Beijing: Science Press.

[5]	Chen M. -F. From Markov Chains to Non-equilibrium Particle Systems, 2004 2nd Ed. Singapore: World Scientific.

[6]	Chen M.-F. Eigenvalues, Inequalities and Ergodic Theory, 2004, New York: Springer.

[7]	Diaconis P., Saloff-Coste L. Nash inequalities for finite Markov chains. J Theor Prob, 1996, 9: 459-510.

[8]	Hou Z. T., Guo Q. F. Homogeneous Denumerable Markov Processes, 1988, Berlin: Springer.

[9]	Kemeny J. G., Snell J. L., Knapp A. W. Denumerable Markov Chains, 1976, New York: Springer-Verlag.

[10]	Mao Y. H. Eigentime identity for ergodic Markov chains. J Appl Probab, 2004, 41: 1071-1080.

[11]	Mao Y. H. Eigentime identity for transient Markov chains. J Math Anal Appl, 2006, 315: 415-424.

[12]	Meyer C. Matrix Analysis and Applied Linear Algebra, 2000, Philadelphia: SIAM.

[13]	Roberts G., Rosenthal J. Shift coupling and convergence rates of ergodic averages. Communications in Statistics-Stochastic Models, 1997, 13: 147-165.