We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metricand show that the finiteness of the expectation E(i,j)[Σ^{τ△-1}_{k=0} *r*(*k*)], where τ△ is the hitting time on thecoupling set △ and* r* is a subgeometric rate function, is equivalent to a sequence of Foster-Lyapunovdrift conditions which imply subgeometric convergence in the Wassertein distance. We give an examplefor a ’family of nested drift conditions’.

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 17)

Pages:

40-45

Citation:

M. Lekgari, "A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric", Bulletin of Mathematical Sciences and Applications, Vol. 17, pp. 40-45, 2016

Online since:

November 2016

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Open Access

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Creative Commons Attribution 4.0 International License

References:

[1] O. Butkovsky, Subgemetric rates of convergence of Markov processes in the Masserstein metric, Ann. Appl. Probab. 24(2) (2014) 526-552.

[2] A. Durmus, G. Fort, E. Moulines, New conditions for subgeometric rates of convergence in the Wasserstein distance for Markov chains, Unpublished paper, 2014. Available on: https: /hal. archives-ouvertes. fr/hal-00948661v1/document.

[3] 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 (1983) 295-311.

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

[5] S.P. Meyn, R.L. Tweedie, State-dependent criteria for convergence of Markov chains, Ann. Appl. Prob. (1994) 149-168.

[6] M.V. Lekgari, Subgeometric Ergodicity Analysis of Continuous-time Markov Chains Under Random-time State-dependent Lyapunov Drift Conditions, J. Prob. Stat. 2014 (2014), Article ID 274535.

[7] S.P. Meyn, R.L. Tweedie, Markov Chains and Stochastic Stability, Springer, (1993).

[8] R.L. Tweedie, Criteria for rates of convergence of Markov chains, in J.F.C. Kingman , G.E.H. Reuter(Eds. ), Probaility Statistics and Analysis, in: London Mathematical Society Lecture Note Series, Cambridge University Press, 1983, pp.227-250.

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