Subscribe

Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

BMSA > Volume 10 > Maximal Coupling Procedure and Stability of...
< Back to Volume

Maximal Coupling Procedure and Stability of Continuous-Time Markov Chains

Full Text PDF

Abstract:

In this study we first investigate the stability of subsampled discrete Markov chains through the use of the maximal coupling procedure. This is an extension of the available results on Markov chains and is realized through the analysis of the subsampled chain ΦΤn, where {Τn, nєZ+}is an increasing sequence of random stopping times. Then the similar results are realized for the stability of countable-state Continuous-time Markov processes by employing the skeleton-chain method.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 10)
Pages:
30-37
DOI:
10.18052/www.scipress.com/BMSA.10.30
Citation:
M. V. Lekgari "Maximal Coupling Procedure and Stability of Continuous-Time Markov Chains", Bulletin of Mathematical Sciences and Applications, Vol. 10, pp. 30-37, 2014
Online since:
Nov 2014
Export:
Distribution:
References:

C. Andrieu, G. Fort, Explicit control of subgeometric ergodicity, Technical Report, Univ. Bristol, 05: 17, 2005. (Available at http: /www. tsi. enst. fr/ gfort/biblio. html).

S.B. Connor, Coupling: Cutoffs, CFTP and Tameness. PhD Thesis, University of Warwick, (2007).

S.B. Connor and G. Fort, State-dependent Foster-Lyapunov criteria for subgeometric convergence of Markov chains, Stochastic Processes and their Applications, 119: 4176-4193, October (2009).

R. Douc, G. Fort,E. Moulines and P. Soulier, Practical drift conditions for subgeometric rates of convergence, Annals of Appl. Prob, 14(3): 1353-1377, (2004).

D. Griffeath, A maximal coupling for Markov chains, Z. Wahrscheinlichkeitstheorie und Verw. Gebeite 31: 360-380, (1975).

M. Hairer, Convergence of Markov processes, Lecture Notes, (2010).

M.V. Kartashov, V.V. Golomozy, Maximal Coupling Procedure and Stability of Dicrete Markov Chains, Theor. Probab. Math. Stat. 86: 93-104, (2012).

T. Lindvall, Lectures on the Coupling Method, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & SonsInc., New York, (1992).

E. Nummelin, P. Tuominen, The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewal theory. Stochastic Process Appl. 15: 295-311, (1983).

G.O. Roberts and J.S. Rosenthal, General State space Markov chains and MCMC algorithms, Probability Survey, 1: 20-71, (2004).

F.M. Spieksma, Kolmogorov forward equation and explosiveness in countable state Markov processes, Ann. Operat. Res. DOI: 10. 1007/s10479-012-1262-7, (2012).

Show More Hide