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Separation cutoff for upward skip-free chains

Published online by Cambridge University Press:  24 March 2016

Y. H. Mao ,
C. Zhang  and
Y. H. Zhang
Y. H. Mao
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China.
Y. H. Zhang
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China.
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Abstract

A computable necessary and sufficient condition of separation cutoff is obtained for a sequence of continuous-time upward skip-free chains with the stochastically monotone time-reversals.

Keywords

Separation cutoffupward skip-free chainstochastic monotonicitystrong stationary timeboundary theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016 , pp. 299 - 306
Copyright
Copyright © Applied Probability Trust 2016 

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References

[1]Aldous, D. and Diaconis, P. (1987). Strong uniform times and finite random walks. Adv. Appl. Math. 8, 69–97. CrossRefGoogle Scholar
[2]Anderson, W. J. (1991). Continuous-Time Markov Chains: An Applications-Oriented Approach. Springer, New York. Google Scholar
[3]Chen, G.-Y. and Saloff-Coste, L. (2010). The L 2-cutoff for reversible Markov processes. J. Funct. Analysis 258, 2246–2315. Google Scholar
[4]Chen, M.-F. (2004). From Markov Chains to Non-Equilibrium Particle Systems, 2nd edn. World Scientific, River Edge, NJ. CrossRefGoogle Scholar
[5]Diaconis, P. (1996). The cutoff phenomenon in finite Markov chains. Proc. Nat. Acad. Sci. USA 93, 1659–1664. CrossRefGoogle ScholarPubMed
[6]Diaconis, P. and Saloff-Coste, L. (2006). Separation cut-offs for birth and death chains. Ann. Appl. Prob. 16, 2098–2122. Google Scholar
[7]Ding, J., Lubetzky, E. and Peres, Y. (2010). Total variation cutoff in birth-and-death chains. Prob. Theory Relat. Fields 146, 61–85. CrossRefGoogle Scholar
[8]Fill, J. A. (1991). Time to stationarity for a continuous-time Markov chain. Prob. Eng. Inf. Sci. 5, 61–76. CrossRefGoogle Scholar
[9]Fill, J. A. (2009). On hitting times and fastest strong stationary times for skip-free and more general chains. J. Theoret. Prob. 22, 587–600. Google Scholar
[10]Mao, Y. (2004). Ergodic degrees for continuous-time Markov chains. Sci. China A 47, 161–174. Google Scholar
[11]Mao, Y. and Zhang, Y. (2014). Explicit criteria on separation cutoff for birth and death chains. Front. Math. China 9, 881–898. Google Scholar
[12]Zhang, Y. H. (2013). Expressions on moments of hitting time for single birth processes in infinite and finite spaces. Beijing Shifan Daxue Xuebao 49, 445–452 (in Chinese). Google Scholar