A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric

Lekgari, Mokaedi

doi:10.18052/www.scipress.com/BMSA.17.40

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A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric

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Abstract:

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’.

Info:

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 17)

Pages:

40-45

DOI:

https://doi.org/10.18052/www.scipress.com/BMSA.17.40

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

Authors:

Mokaedi Lekgari

Keywords:

Ergodicity, Markov Chains, Wasserstein Metric

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Open Access

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Creative Commons Attribution 4.0 International License

References:

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[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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